diff --git a/.circleci/config.yml b/.circleci/config.yml
index 7949f83138c5727bec74d23e6f8c372cc94184f4..d33849e40ed5093b194e471b335020955ffee8b6 100644
--- a/.circleci/config.yml
+++ b/.circleci/config.yml
@@ -106,8 +106,8 @@ jobs:
             # If nixpkgs changes then potentially a lot of cached packages for
             # the base system will be invalidated so we may as well drop them
             # and make a new cache with the new packages.
-            - zkapauthorizer-nix-store-v3-{{ checksum "nixpkgs.rev" }}
-            - zkapauthorizer-nix-store-v3-
+            - zkapauthorizer-nix-store-v4-{{ checksum "nixpkgs.rev" }}
+            - zkapauthorizer-nix-store-v4-
 
       - run:
           name: "Run Test Suite"
@@ -122,7 +122,10 @@ jobs:
             #
             # Further, we want the "doc" output built as well because that's
             # where the coverage data ends up.
-            nix-build --argstr hypothesisProfile ci --arg collectCoverage true --attr doc
+            #
+            # Also limit the number of concurrent jobs because of resource
+            # constraints on CircleCI. :/
+            nix-build --cores 1 --max-jobs 1 --argstr hypothesisProfile ci --arg collectCoverage true --attr doc
 
       - run:
           name: "Cache codecov"
@@ -136,15 +139,14 @@ jobs:
 
       - save_cache:
           name: "Cache Nix Store Paths"
-          key: zkapauthorizer-nix-store-v3-{{ checksum "nixpkgs.rev" }}
+          key: zkapauthorizer-nix-store-v4-{{ checksum "nixpkgs.rev" }}
           paths:
             - "/nix"
 
       - run:
           name: "Report Coverage"
           command: |
-            nix-shell -p 'python.withPackages (ps: [ ps.codecov ])' --run \
-              'codecov --file ./result-doc/share/doc/*/.coverage'
+            ./.circleci/report-coverage.sh
 
 workflows:
   version: 2
diff --git a/.circleci/report-coverage.sh b/.circleci/report-coverage.sh
new file mode 100755
index 0000000000000000000000000000000000000000..3f15868363d5f8b3c1db8f1b6d591e5862efe971
--- /dev/null
+++ b/.circleci/report-coverage.sh
@@ -0,0 +1,9 @@
+#! /usr/bin/env nix-shell
+#! nix-shell -i bash -p "python.withPackages (ps: [ ps.codecov ])"
+set -x
+find ./result-doc/share/doc
+cp ./result-doc/share/doc/*/.coverage.* ./
+python -m coverage combine
+python -m coverage report
+python -m coverage xml
+codecov --file coverage.xml
diff --git a/.coveragerc b/.coveragerc
index ec19cb88f397c327bac1afa6a195073f305e3e3d..4d27672886ff83d00efb47c63e2aa77e3819d1c3 100644
--- a/.coveragerc
+++ b/.coveragerc
@@ -3,4 +3,33 @@ source =
     _zkapauthorizer
     twisted.plugins.zkapauthorizer
 
+# Measuring branch coverage is slower (so the conventional wisdom goes) but
+# too bad: it's an important part of the coverage information.
 branch = True
+
+# Whether or not we actually collect coverage information in parallel, we need
+# to have the coverage data files written according to the "parallel" naming
+# scheme so that we can use "coverage combine" later to rewrite paths in the
+# coverage report.
+parallel = True
+
+omit =
+# The Versioneer version file in the repository is generated by
+# Versioneer.  Let's call it Versioneer's responsibility to ensure it
+# works and not pay attention to our test suite's coverage of it.  Also,
+# the way Versioneer works is that the source file in the repository is
+# different from the source file in an installation - which is where we
+# measure coverage.  When the source files differ like this, it's very
+# difficult to produce a coherent coverage report (measurements against
+# one source file are meaningless when looking at a different source
+# file).
+    */_zkapauthorizer/_version.py
+
+[paths]
+source =
+# It looks like this in the checkout
+    src/
+# It looks like this in the Nix build environment
+    /nix/store/*/lib/python*/site-packages/
+# It looks like this in the Windows build environment
+    C:\hostedtoolcache\windows\Python\2.7.18\x64\Lib\site-packages\
diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index b64117daf8257230e49ce1c955088a44707702b1..c8995972397b0b4eee5e00b527d99897cf39050c 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -37,23 +37,19 @@ jobs:
 
     - name: "Upgrade Pip"
       run: |
-        python -m pip install --upgrade pip
+        python -m pip install -v --upgrade pip
 
     - name: "Install CI Dependencies"
       run: |
-        python -m pip install wheel coverage
-
-    - name: "Install Tahoe-LAFS master@HEAD"
-      run: |
-        python -m pip install git+https://github.com/tahoe-lafs/tahoe-lafs@master#egg=tahoe-lafs
+        python -m pip install -v wheel coverage
 
     - name: "Install Test Dependencies"
       run: |
-        python -m pip install -r test-requirements.txt
+        python -m pip install -v -r test-requirements.txt
 
     - name: "Install ZKAPAuthorizer"
       run: |
-        python -m pip install ./
+        python -m pip install -v ./
 
     - name: "Dump Python Environment"
       run: |
@@ -63,11 +59,17 @@ jobs:
       env:
         MAGIC_FOLDER_HYPOTHESIS_PROFILE: "ci"
       run: |
-        python -m coverage run -m twisted.trial _zkapauthorizer
-
+        python -m coverage run --debug=config -m twisted.trial _zkapauthorizer
 
     - name: "Convert Coverage"
       run: |
+        echo "Files:"
+        dir
+        echo "Combining"
+        coverage combine
+        echo "Reporting"
+        coverage report
+        echo "Converting to XML"
         coverage xml
 
     - uses: codecov/codecov-action@v1
diff --git a/eliot.nix b/eliot.nix
deleted file mode 100644
index f6d6b3061b1ea635bac0e694be407ca8d1b6befb..0000000000000000000000000000000000000000
--- a/eliot.nix
+++ /dev/null
@@ -1,27 +0,0 @@
-{ lib, buildPythonPackage, fetchPypi, zope_interface, pyrsistent, boltons
-, hypothesis, testtools, pytest }:
-buildPythonPackage rec {
-  pname = "eliot";
-  version = "1.7.0";
-
-  src = fetchPypi {
-    inherit pname version;
-    sha256 = "0ylyycf717s5qsrx8b9n6m38vyj2k8328lfhn8y6r31824991wv8";
-  };
-
-  postPatch = ''
-    substituteInPlace setup.py \
-      --replace "boltons >= 19.0.1" boltons
-    # depends on eliot.prettyprint._main which we don't have here.
-    rm eliot/tests/test_prettyprint.py
-  '';
-
-  checkInputs = [ testtools pytest hypothesis ];
-  propagatedBuildInputs = [ zope_interface pyrsistent boltons ];
-
-  meta = with lib; {
-    homepage = https://github.com/itamarst/eliot/;
-    description = "Logging library that tells you why it happened";
-    license = licenses.asl20;
-  };
-}
diff --git a/nix/setup.cfg.patch b/nix/setup.cfg.patch
new file mode 100644
index 0000000000000000000000000000000000000000..c2cdeea1617d10691e9b151d1b3b1308c451952f
--- /dev/null
+++ b/nix/setup.cfg.patch
@@ -0,0 +1,13 @@
+diff --git a/setup.cfg b/setup.cfg
+index dfc49607..822ea8dd 100644
+--- a/setup.cfg
++++ b/setup.cfg
+@@ -40,7 +40,7 @@ install_requires =
+     # incompatible with Tahoe-LAFS'.  So duplicate them here (the ones that
+     # have been observed to cause problems).
+     Twisted[tls,conch]>=18.4.0
+-    tahoe-lafs==1.14.0
++    tahoe-lafs
+     treq
+ 
+ [versioneer]
diff --git a/overlays.nix b/overlays.nix
index ed2d8d1af449fcc410a0182b9d26e5b2a868e858..3d548fade895e7a390596fd56861d37ed753c5dc 100644
--- a/overlays.nix
+++ b/overlays.nix
@@ -15,12 +15,9 @@ self: super: {
       # 2 support.
       typing = python-self.callPackage ./typing.nix { };
 
-      # new tahoe-lafs dependency
-      eliot = python-self.callPackage ./eliot.nix { };
-
       # tahoe-lafs in nixpkgs is packaged as an application!  so we have to
       # re-package it ourselves as a library.
-      tahoe-lafs = python-self.callPackage ((import ./tahoe-lafs.nix) + "/nix") { };
+      tahoe-lafs = python-self.callPackage ./tahoe-lafs.nix { };
 
       # we depend on the challenge-bypass-ristretto python package, a set of
       # bindings to the challenge-bypass-ristretto Rust crate.
diff --git a/setup.cfg b/setup.cfg
index 371a19b343c204fb576b2c6d8c77d969160d40e3..dfc4960747ba2d57bea9b12deff72f59371cd743 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -36,9 +36,11 @@ install_requires =
     eliot
     aniso8601
     python-challenge-bypass-ristretto
-    # Inherit our Twisted dependency from tahoe-lafs so we don't accidentally
-    # get the extras wrong here and break stuff.
-    tahoe-lafs
+    # The pip resolver sometimes finds treq's dependencies first and these are
+    # incompatible with Tahoe-LAFS'.  So duplicate them here (the ones that
+    # have been observed to cause problems).
+    Twisted[tls,conch]>=18.4.0
+    tahoe-lafs==1.14.0
     treq
 
 [versioneer]
diff --git a/src/_zkapauthorizer/_storage_server.py b/src/_zkapauthorizer/_storage_server.py
index a2d4b9f2c5cce038eff98184ae4859cbde8f8b81..7aa17c840a705ffb15a656a8f85befda42836781 100644
--- a/src/_zkapauthorizer/_storage_server.py
+++ b/src/_zkapauthorizer/_storage_server.py
@@ -42,6 +42,7 @@ from os.path import (
 )
 from os import (
     listdir,
+    stat,
 )
 from datetime import (
     timedelta,
@@ -517,23 +518,50 @@ def get_storage_index_share_size(sharepath):
 
     :return int: The data size of the share in bytes.
     """
-    # Note Tahoe-LAFS immutable/layout.py makes some claims about how the
-    # share data is structured.  A lot of this seems to be wrong.
-    # storage/immutable.py appears to have the correct information.
-    fmt = ">LL"
+    # From src/allmydata/storage/immutable.py
+    #
+    # The share file has the following layout:
+    #  0x00: share file version number, four bytes, current version is 1
+    #  0x04: share data length, four bytes big-endian = A # See Footnote 1 below.
+    #  0x08: number of leases, four bytes big-endian
+    #  0x0c: beginning of share data (see immutable.layout.WriteBucketProxy)
+    #  A+0x0c = B: first lease. Lease format is:
+    #   B+0x00: owner number, 4 bytes big-endian, 0 is reserved for no-owner
+    #   B+0x04: renew secret, 32 bytes (SHA256)
+    #   B+0x24: cancel secret, 32 bytes (SHA256)
+    #   B+0x44: expiration time, 4 bytes big-endian seconds-since-epoch
+    #   B+0x48: next lease, or end of record
+    #
+    # Footnote 1: as of Tahoe v1.3.0 this field is not used by storage
+    # servers, but it is still filled in by storage servers in case the
+    # storage server software gets downgraded from >= Tahoe v1.3.0 to < Tahoe
+    # v1.3.0, or the share file is moved from one storage server to
+    # another. The value stored in this field is truncated, so if the actual
+    # share data length is >= 2**32, then the value stored in this field will
+    # be the actual share data length modulo 2**32.
+
+    share_file_size = stat(sharepath).st_size
+    header_format = ">LLL"
+    header_size = calcsize(header_format)
     with open(sharepath, "rb") as share_file:
-        header = share_file.read(calcsize(fmt))
+        header = share_file.read(calcsize(header_format))
 
-    if len(header) != calcsize(fmt):
+    if len(header) != header_size:
         raise ValueError(
             "Tried to read {} bytes of share file header, got {!r} instead.".format(
-                calcsize(fmt),
+                calcsize(header_format),
                 header,
             ),
         )
 
-    version, share_data_length = unpack(fmt, header)
-    return share_data_length
+    version, _, number_of_leases = unpack(header_format, header)
+
+    if version != 1:
+        raise ValueError(
+            "Cannot interpret version {} share file.".format(version),
+        )
+
+    return share_file_size - header_size - (number_of_leases * (4 + 32 + 32 + 4))
 
 
 def get_lease_expiration(get_leases, storage_index_or_slot):
diff --git a/src/_zkapauthorizer/tests/storage_common.py b/src/_zkapauthorizer/tests/storage_common.py
index 4baf4de7b89ff6ab3c0ea7145b5d0fa347f3a8e9..d00a580c29adf51f1d39583012fbe09b11555678 100644
--- a/src/_zkapauthorizer/tests/storage_common.py
+++ b/src/_zkapauthorizer/tests/storage_common.py
@@ -16,6 +16,13 @@
 ``allmydata.storage``-related helpers shared across the test suite.
 """
 
+from os import (
+    SEEK_CUR,
+)
+from struct import (
+    pack,
+)
+
 from twisted.python.filepath import (
     FilePath,
 )
@@ -25,6 +32,9 @@ from .strategies import (
     bytes_for_share,
 )
 
+# Hard-coded in Tahoe-LAFS
+LEASE_INTERVAL = 60 * 60 * 24 * 31
+
 def cleanup_storage_server(storage_server):
     """
     Delete all of the shares held by the given storage server.
@@ -73,3 +83,53 @@ def write_toy_shares(
     for (sharenum, writer) in allocated.items():
         writer.remote_write(0, bytes_for_share(sharenum, size))
         writer.remote_close()
+
+
+def whitebox_write_sparse_share(sharepath, version, size, leases, now):
+    """
+    Write a zero-filled sparse (if the filesystem supports it) immutable share
+    to the given path.
+
+    This assumes knowledge of the Tahoe-LAFS share file format.
+
+    :param FilePath sharepath: The path to which to write the share file.
+    :param int version: The share version to write to the file.
+    :param int size: The share data size to write.
+    :param list leases: Renewal secrets for leases to write to the share file.
+    :param float now: The current time as a POSIX timestamp.
+    """
+    # Maybe-saturated size (what at least one Tahoe-LAFS comment claims is
+    # appropriate for large files)
+    internal_size = min(size, 2 ** 32 - 1)
+    apparent_size = size
+
+    header_format = ">LLL"
+    lease_format = ">L32s32sL"
+    with sharepath.open("wb") as share:
+        share.write(
+            pack(
+                header_format,
+                version,
+                internal_size,
+                len(leases),
+            ),
+        )
+        # Try to make it sparse by skipping all the data.
+        share.seek(apparent_size - 1, SEEK_CUR),
+        share.write(b"\0")
+        share.write(
+            b"".join(
+                pack(
+                    lease_format,
+                    # no owner
+                    0,
+                    renew,
+                    # no cancel secret
+                    b"",
+                    # expiration timestamp
+                    int(now + LEASE_INTERVAL),
+                )
+                for renew
+                in leases
+            ),
+        )
diff --git a/src/_zkapauthorizer/tests/strategies.py b/src/_zkapauthorizer/tests/strategies.py
index 3baf11475b7daa296d8ef621ba493175238a3a45..a438fa27ae10bd937f6e30421297da297fc753f6 100644
--- a/src/_zkapauthorizer/tests/strategies.py
+++ b/src/_zkapauthorizer/tests/strategies.py
@@ -524,6 +524,13 @@ def write_enabler_secrets():
     )
 
 
+def share_versions():
+    """
+    Build integers which could be Tahoe-LAFS share file version numbers.
+    """
+    return integers(min_value=0, max_value=2 ** 32 - 1)
+
+
 def sharenums():
     """
     Build Tahoe-LAFS share numbers.
@@ -545,17 +552,19 @@ def sharenum_sets():
     )
 
 
-def sizes():
+def sizes(
+    # Size 0 data isn't data, it's nothing.
+    min_value=1,
+    # Let this be larger than a single segment (2 ** 17) in case that matters
+    # to Tahoe-LAFS storage at all.  I don't think it does, though.
+    max_value=2 ** 18,
+):
     """
     Build Tahoe-LAFS share sizes.
     """
     return integers(
-        # Size 0 data isn't data, it's nothing.
-        min_value=1,
-        # Let this be larger than a single segment (2 ** 17) in case that
-        # matters to Tahoe-LAFS storage at all.  I don't think it does,
-        # though.
-        max_value=2 ** 18,
+        min_value=min_value,
+        max_value=max_value,
     )
 
 
diff --git a/src/_zkapauthorizer/tests/test_storage_protocol.py b/src/_zkapauthorizer/tests/test_storage_protocol.py
index f2b9b6895246583018d498422e84ad2265e4eb4c..a267c0667f3fe1b3101ab9e5a7a9eb10d8091a32 100644
--- a/src/_zkapauthorizer/tests/test_storage_protocol.py
+++ b/src/_zkapauthorizer/tests/test_storage_protocol.py
@@ -70,6 +70,10 @@ from challenge_bypass_ristretto import (
     random_signing_key,
 )
 
+from allmydata.storage.common import (
+    storage_index_to_dir,
+)
+
 from .common import (
     skipIf,
 )
@@ -82,6 +86,7 @@ from .strategies import (
     lease_renew_secrets,
     lease_cancel_secrets,
     write_enabler_secrets,
+    share_versions,
     sharenums,
     sharenum_sets,
     sizes,
@@ -97,8 +102,10 @@ from .fixtures import (
     AnonymousStorageServer,
 )
 from .storage_common import (
+    LEASE_INTERVAL,
     cleanup_storage_server,
     write_toy_shares,
+    whitebox_write_sparse_share,
 )
 from .foolscap import (
     LocalRemote,
@@ -119,7 +126,6 @@ from ..foolscap import (
     ShareStat,
 )
 
-
 class RequiredPassesTests(TestCase):
     """
     Tests for ``required_passes``.
@@ -353,19 +359,7 @@ class ShareTests(TestCase):
             Equals(int(now + self.server.LEASE_PERIOD.total_seconds())),
         )
 
-    @given(
-        storage_index=storage_indexes(),
-        renew_secret=lease_renew_secrets(),
-        cancel_secret=lease_cancel_secrets(),
-        sharenum=sharenums(),
-        size=sizes(),
-        clock=clocks(),
-    )
-    def test_stat_shares_immutable(self, storage_index, renew_secret, cancel_secret, sharenum, size, clock):
-        """
-        Size and lease information about immutable shares can be retrieved from a
-        storage server.
-        """
+    def _stat_shares_immutable_test(self, storage_index, sharenum, size, clock, leases, write_shares):
         # Hypothesis causes our storage server to be used many times.  Clean
         # up between iterations.
         cleanup_storage_server(self.anonymous_storage_server)
@@ -376,23 +370,27 @@ class ShareTests(TestCase):
         try:
             patch.setUp()
             # Create a share we can toy with.
-            write_toy_shares(
+            write_shares(
                 self.anonymous_storage_server,
                 storage_index,
-                renew_secret,
-                cancel_secret,
                 {sharenum},
                 size,
                 canary=self.canary,
             )
+            # Perhaps put some more leases on it.  Leases might impact our
+            # ability to determine share data size.
+            for renew_secret in leases:
+                self.anonymous_storage_server.remote_add_lease(
+                    storage_index,
+                    renew_secret,
+                    b"",
+                )
         finally:
             patch.cleanUp()
 
         stats = extract_result(
             self.client.stat_shares([storage_index]),
         )
-        # Hard-coded in Tahoe-LAFS
-        LEASE_INTERVAL = 60 * 60 * 24 * 31
         expected = [{
             sharenum: ShareStat(
                 size=size,
@@ -404,6 +402,172 @@ class ShareTests(TestCase):
             Equals(expected),
         )
 
+    @given(
+        storage_index=storage_indexes(),
+        renew_secret=lease_renew_secrets(),
+        cancel_secret=lease_cancel_secrets(),
+        sharenum=sharenums(),
+        size=sizes(),
+        clock=clocks(),
+        leases=lists(lease_renew_secrets(), unique=True),
+    )
+    def test_stat_shares_immutable(self, storage_index, renew_secret, cancel_secret, sharenum, size, clock, leases):
+        """
+        Size and lease information about immutable shares can be retrieved from a
+        storage server.
+        """
+        return self._stat_shares_immutable_test(
+            storage_index,
+            sharenum,
+            size,
+            clock,
+            leases,
+            lambda storage_server, storage_index, sharenums, size, canary: write_toy_shares(
+                storage_server,
+                storage_index,
+                renew_secret,
+                cancel_secret,
+                sharenums,
+                size,
+                canary,
+            ),
+        )
+
+    @given(
+        storage_index=storage_indexes(),
+        sharenum=sharenums(),
+        size=sizes(),
+        clock=clocks(),
+        leases=lists(lease_renew_secrets(), unique=True, min_size=1),
+        version=share_versions(),
+    )
+    def test_stat_shares_immutable_wrong_version(self, storage_index, sharenum, size, clock, leases, version):
+        """
+        If a share file with an unexpected version is found, ``stat_shares``
+        declines to offer a result (by raising ``ValueError``).
+        """
+        assume(version != 1)
+
+        # Hypothesis causes our storage server to be used many times.  Clean
+        # up between iterations.
+        cleanup_storage_server(self.anonymous_storage_server)
+
+        sharedir = FilePath(self.anonymous_storage_server.sharedir).preauthChild(
+            # storage_index_to_dir likes to return multiple segments
+            # joined by pathsep
+            storage_index_to_dir(storage_index),
+        )
+        sharepath = sharedir.child(u"{}".format(sharenum))
+        sharepath.parent().makedirs()
+        whitebox_write_sparse_share(
+            sharepath,
+            version=version,
+            size=size,
+            leases=leases,
+            now=clock.seconds(),
+        )
+
+        self.assertThat(
+            self.client.stat_shares([storage_index]),
+            failed(
+                AfterPreprocessing(
+                    lambda f: f.value,
+                    IsInstance(ValueError),
+                ),
+            ),
+        )
+
+    @given(
+        storage_index=storage_indexes(),
+        sharenum=sharenums(),
+        size=sizes(),
+        clock=clocks(),
+        version=share_versions(),
+        # Encode our knowledge of the share header format and size right here...
+        position=integers(min_value=0, max_value=11),
+    )
+    def test_stat_shares_truncated_file(self, storage_index, sharenum, size, clock, version, position):
+        """
+        If a share file is truncated in the middle of the header,
+        ``stat_shares`` declines to offer a result (by raising
+        ``ValueError``).
+        """
+        # Hypothesis causes our storage server to be used many times.  Clean
+        # up between iterations.
+        cleanup_storage_server(self.anonymous_storage_server)
+
+        sharedir = FilePath(self.anonymous_storage_server.sharedir).preauthChild(
+            # storage_index_to_dir likes to return multiple segments
+            # joined by pathsep
+            storage_index_to_dir(storage_index),
+        )
+        sharepath = sharedir.child(u"{}".format(sharenum))
+        sharepath.parent().makedirs()
+        whitebox_write_sparse_share(
+            sharepath,
+            version=version,
+            size=size,
+            # We know leases are at the end, where they'll get chopped off, so
+            # we don't bother to write any.
+            leases=[],
+            now=clock.seconds(),
+        )
+        with sharepath.open("wb") as fobj:
+            fobj.truncate(position)
+
+        self.assertThat(
+            self.client.stat_shares([storage_index]),
+            failed(
+                AfterPreprocessing(
+                    lambda f: f.value,
+                    IsInstance(ValueError),
+                ),
+            ),
+        )
+
+
+    @skipIf(platform.isWindows(), "Creating large files on Windows (no sparse files) is too slow")
+    @given(
+        storage_index=storage_indexes(),
+        sharenum=sharenums(),
+        size=sizes(min_value=2 ** 18, max_value=2 ** 40),
+        clock=clocks(),
+        leases=lists(lease_renew_secrets(), unique=True, min_size=1),
+    )
+    def test_stat_shares_immutable_large(self, storage_index, sharenum, size, clock, leases):
+        """
+        Size and lease information about very large immutable shares can be
+        retrieved from a storage server.
+
+        This is more of a whitebox test.  It assumes knowledge of Tahoe-LAFS
+        share placement and layout.  This is necessary to avoid having to
+        write real multi-gigabyte files to exercise the behavior.
+        """
+        def write_shares(storage_server, storage_index, sharenums, size, canary):
+            sharedir = FilePath(storage_server.sharedir).preauthChild(
+                # storage_index_to_dir likes to return multiple segments
+                # joined by pathsep
+                storage_index_to_dir(storage_index),
+            )
+            for sharenum in sharenums:
+                sharepath = sharedir.child(u"{}".format(sharenum))
+                sharepath.parent().makedirs()
+                whitebox_write_sparse_share(
+                    sharepath,
+                    version=1,
+                    size=size,
+                    leases=leases,
+                    now=clock.seconds(),
+                )
+
+        return self._stat_shares_immutable_test(
+            storage_index,
+            sharenum,
+            size,
+            clock,
+            leases,
+            write_shares,
+        )
 
     @skipIf(platform.isWindows(), "Storage server miscomputes slot size on Windows")
     @given(
@@ -454,8 +618,6 @@ class ShareTests(TestCase):
         stats = extract_result(
             self.client.stat_shares([storage_index]),
         )
-        # Hard-coded in Tahoe-LAFS
-        LEASE_INTERVAL = 60 * 60 * 24 * 31
         expected = [{
             sharenum: ShareStat(
                 size=get_implied_data_length(
diff --git a/tahoe-lafs-repo.nix b/tahoe-lafs-repo.nix
new file mode 100644
index 0000000000000000000000000000000000000000..fc944e5739e7246a922761b2c7abaf05b62b8327
--- /dev/null
+++ b/tahoe-lafs-repo.nix
@@ -0,0 +1,9 @@
+let
+  pkgs = import <nixpkgs> {};
+in
+  pkgs.fetchFromGitHub {
+    owner = "tahoe-lafs";
+    repo = "tahoe-lafs";
+    rev = "tahoe-lafs-1.14.0";
+    sha256 = "1ahdiapg57g6icv7p2wbzgkwl9lzdlgrsvbm5485414m7z2d6las";
+  }
diff --git a/tahoe-lafs.nix b/tahoe-lafs.nix
index c305267b8914012921a9896a2e42ef2560f42a38..212439638fb54e1dfb57d5ae91784759e234d02e 100644
--- a/tahoe-lafs.nix
+++ b/tahoe-lafs.nix
@@ -1,9 +1,20 @@
+{ python2Packages }:
 let
-  pkgs = import <nixpkgs> {};
+  # Manually assemble the tahoe-lafs build inputs because tahoe-lafs 1.14.0
+  # eliot package runs the eliot test suite which is flaky.  Doing this gives
+  # us a place to insert a `doCheck = false` (at the cost of essentially
+  # duplicating tahoe-lafs' default.nix).  Not ideal but at least we can throw
+  # it away when we upgrade to the next tahoe-lafs version.
+  repo = ((import ./tahoe-lafs-repo.nix) + "/nix");
+  nevow-drv = repo + "/nevow.nix";
+  nevow = python2Packages.callPackage nevow-drv { };
+  eliot-drv = repo + "/eliot.nix";
+  eliot = (python2Packages.callPackage eliot-drv { }).overrideAttrs (old: {
+    doInstallCheck = false;
+  });
+  tahoe-lafs-drv = repo + "/tahoe-lafs.nix";
+  tahoe-lafs = python2Packages.callPackage tahoe-lafs-drv {
+    inherit nevow eliot;
+  };
 in
-  pkgs.fetchFromGitHub {
-    owner = "tahoe-lafs";
-    repo = "tahoe-lafs";
-    rev = "34aeefd3ddbf28dafbc3477e52461eafa53b545d";
-    sha256 = "0l8n4njbzgiwmn3qsmvzyzqlb0y9bj9g2jvpdynvsn1ggxrqmvsq";
-  }
\ No newline at end of file
+  tahoe-lafs
diff --git a/zkapauthorizer.nix b/zkapauthorizer.nix
index a5e611b4c8879f65aa12c63c968de225a96834ac..89639e0d41ec84db5811503dd150f9c33250d0a3 100644
--- a/zkapauthorizer.nix
+++ b/zkapauthorizer.nix
@@ -1,6 +1,6 @@
 { lib
 , buildPythonPackage, sphinx, git
-, attrs, zope_interface, eliot, aniso8601, twisted, tahoe-lafs, challenge-bypass-ristretto, treq
+, attrs, zope_interface, aniso8601, twisted, tahoe-lafs, challenge-bypass-ristretto, treq
 , fixtures, testtools, hypothesis, pyflakes, coverage
 , hypothesisProfile ? null
 , collectCoverage ? false
@@ -27,11 +27,18 @@ buildPythonPackage rec {
     sphinx
   ];
 
+  patches = [
+    # Remove the Tahoe-LAFS version pin in distutils config.  We have our own
+    # pinning and also our Tahoe-LAFS package has a bogus version number. :/
+    ./nix/setup.cfg.patch
+  ];
+
   propagatedBuildInputs = [
     attrs
     zope_interface
     aniso8601
-    eliot
+    # Inherit eliot from tahoe-lafs
+    # eliot
     twisted
     tahoe-lafs
     challenge-bypass-ristretto
@@ -49,7 +56,7 @@ buildPythonPackage rec {
     runHook preCheck
     "${pyflakes}/bin/pyflakes" src/_zkapauthorizer
     ZKAPAUTHORIZER_HYPOTHESIS_PROFILE=${hypothesisProfile'} python -m ${if collectCoverage
-      then "coverage run --branch --source _zkapauthorizer,twisted.plugins.zkapauthorizer --module"
+      then "coverage run --debug=config --module"
       else ""
     } twisted.trial ${extraTrialArgs} ${testSuite'}
     runHook postCheck
@@ -57,10 +64,8 @@ buildPythonPackage rec {
 
   postCheck = if collectCoverage
     then ''
-    python -m coverage html
     mkdir -p "$doc/share/doc/${name}"
-    cp -vr .coverage htmlcov "$doc/share/doc/${name}"
-    python -m coverage report
+    cp -v .coverage.* "$doc/share/doc/${name}"
     ''
     else "";
 }