diff --git a/coverage/sqldata.py b/coverage/sqldata.py
index 6b3f0dbff..314d4c86b 100644
--- a/coverage/sqldata.py
+++ b/coverage/sqldata.py
@@ -18,6 +18,7 @@
 import sys
 import textwrap
 import threading
+import uuid
 import zlib
 from collections.abc import Collection, Mapping, Sequence
 from typing import Any, Callable, cast
@@ -263,7 +264,7 @@ def _debug_dataio(self, msg: str, filename: str) -> None:
     def _choose_filename(self) -> None:
         """Set self._filename based on inited attributes."""
         if self._no_disk:
-            self._filename = ":memory:"
+            self._filename = f"file:coverage-{uuid.uuid4()}?mode=memory&cache=shared"
         else:
             self._filename = self._basename
             suffix = filename_suffix(self._suffix)
@@ -289,7 +290,7 @@ def close(self, force: bool = False) -> None:
     def _open_db(self) -> None:
         """Open an existing db file, and read its metadata."""
         self._debug_dataio("Opening data file", self._filename)
-        self._dbs[threading.get_ident()] = SqliteDb(self._filename, self._debug)
+        self._dbs[threading.get_ident()] = SqliteDb(self._filename, self._debug, self._no_disk)
         self._read_db()
 
     def _read_db(self) -> None:
@@ -402,7 +403,7 @@ def loads(self, data: bytes) -> None:
                 f"Unrecognized serialization: {data[:40]!r} (head of {len(data)} bytes)",
             )
         script = zlib.decompress(data[1:]).decode("utf-8")
-        self._dbs[threading.get_ident()] = db = SqliteDb(self._filename, self._debug)
+        self._dbs[threading.get_ident()] = db = SqliteDb(self._filename, self._debug, self._no_disk)
         with db:
             db.executescript(script)
         self._read_db()
diff --git a/coverage/sqlitedb.py b/coverage/sqlitedb.py
index 544594eb8..c80702290 100644
--- a/coverage/sqlitedb.py
+++ b/coverage/sqlitedb.py
@@ -28,9 +28,10 @@ class SqliteDb:
                     etc(a, b)
 
     """
-    def __init__(self, filename: str, debug: TDebugCtl) -> None:
+    def __init__(self, filename: str, debug: TDebugCtl, no_disk: bool = False) -> None:
         self.debug = debug
         self.filename = filename
+        self.no_disk = no_disk
         self.nest = 0
         self.con: sqlite3.Connection | None = None
 
@@ -49,7 +50,11 @@ def _connect(self) -> None:
         if self.debug.should("sql"):
             self.debug.write(f"Connecting to {self.filename!r}")
         try:
-            self.con = sqlite3.connect(self.filename, check_same_thread=False)
+            # Use uri=True when connecting to memory URIs
+            if self.filename.startswith("file:"):
+                self.con = sqlite3.connect(self.filename, check_same_thread=False, uri=True)
+            else:
+                self.con = sqlite3.connect(self.filename, check_same_thread=False)
         except sqlite3.Error as exc:
             raise DataError(f"Couldn't use data file {self.filename!r}: {exc}") from exc
 
@@ -78,7 +83,7 @@ def _connect(self) -> None:
     def close(self, force: bool = False) -> None:
         """If needed, close the connection."""
         if self.con is not None:
-            if force or self.filename != ":memory:":
+            if force or not self.no_disk:
                 if self.debug.should("sql"):
                     self.debug.write(f"Closing {self.con!r} on {self.filename!r}")
                 self.con.close()
@@ -120,7 +125,7 @@ def _execute(self, sql: str, parameters: Iterable[Any]) -> sqlite3.Cursor:
                 return self.con.execute(sql, parameters)    # type: ignore[arg-type]
         except sqlite3.Error as exc:
             msg = str(exc)
-            if self.filename != ":memory:":
+            if not self.no_disk:
                 try:
                     # `execute` is the first thing we do with the database, so try
                     # hard to provide useful hints if something goes wrong now.