diff --git a/datasette/database.py b/datasette/database.py
index af1df0a8..dfca179c 100644
--- a/datasette/database.py
+++ b/datasette/database.py
@@ -47,6 +47,8 @@ class Database:
         # These are used when in non-threaded mode:
         self._read_connection = None
         self._write_connection = None
+        # This is used to track all file connections so they can be closed
+        self._all_file_connections = []
 
     @property
     def cached_table_counts(self):
@@ -91,9 +93,16 @@ class Database:
         assert not (write and not self.is_mutable)
         if write:
             qs = ""
-        return sqlite3.connect(
+        conn = sqlite3.connect(
             f"file:{self.path}{qs}", uri=True, check_same_thread=False
         )
+        self._all_file_connections.append(conn)
+        return conn
+
+    def close(self):
+        # Close all connections - useful to avoid running out of file handles in tests
+        for connection in self._all_file_connections:
+            connection.close()
 
     async def execute_write(self, sql, params=None, block=True):
         def _inner(conn):
diff --git a/docs/internals.rst b/docs/internals.rst
index c3892a7c..cc6de867 100644
--- a/docs/internals.rst
+++ b/docs/internals.rst
@@ -874,6 +874,13 @@ If your function raises an exception that exception will be propagated up to the
 
 If you specify ``block=False`` the method becomes fire-and-forget, queueing your function to be executed and then allowing your code after the call to ``.execute_write_fn()`` to continue running while the underlying thread waits for an opportunity to run your function. A UUID representing the queued task will be returned. Any exceptions in your code will be silently swallowed.
 
+.. _database_close:
+
+db.close()
+----------
+
+Closes all of the open connections to file-backed databases. This is mainly intended to be used by large test suites, to avoid hitting limits on the number of open files.
+
 .. _internals_database_introspection:
 
 Database introspection
diff --git a/tests/fixtures.py b/tests/fixtures.py
index 92a10da6..ba5f065e 100644
--- a/tests/fixtures.py
+++ b/tests/fixtures.py
@@ -1,5 +1,5 @@
 from datasette.app import Datasette
-from datasette.utils.sqlite import sqlite3, sqlite_version
+from datasette.utils.sqlite import sqlite3
 from datasette.utils.testing import TestClient
 import click
 import contextlib
@@ -9,11 +9,9 @@ import os
 import pathlib
 import pytest
 import random
-import sys
 import string
 import tempfile
 import textwrap
-import time
 
 
 # This temp file is used by one of the plugin config tests
@@ -167,7 +165,11 @@ def make_app_client(
             crossdb=crossdb,
         )
         yield TestClient(ds)
-        os.remove(filepath)
+        # Close as many database connections as possible
+        # to try and avoid too many open files error
+        for db in ds.databases.values():
+            if not db.is_memory:
+                db.close()
 
 
 @pytest.fixture(scope="session")