diff --git a/src/httpcore2/httpcore2/_backends/anyio.py b/src/httpcore2/httpcore2/_backends/anyio.py
index 16c270e8..20f825ee 100644
--- a/src/httpcore2/httpcore2/_backends/anyio.py
+++ b/src/httpcore2/httpcore2/_backends/anyio.py
@@ -10,11 +10,13 @@
 from .._exceptions import (
     ConnectError,
     ConnectTimeout,
+    ExceptionMapping,
     ReadError,
     ReadTimeout,
     WriteError,
     WriteTimeout,
     map_exceptions,
+    map_timeout,
 )
 from .._utils import is_socket_readable
 from .base import SOCKET_OPTION, AsyncNetworkBackend, AsyncNetworkStream
@@ -25,8 +27,8 @@ def __init__(self, stream: anyio.abc.ByteStream) -> None:
         self._stream = stream
 
     async def read(self, max_bytes: int, timeout: float | None = None) -> bytes:
-        exc_map: dict[type[Exception], type[Exception]] = {
-            TimeoutError: ReadTimeout,
+        exc_map: ExceptionMapping = {
+            TimeoutError: map_timeout(ReadTimeout),
             anyio.BrokenResourceError: ReadError,
             anyio.ClosedResourceError: ReadError,
             anyio.EndOfStream: ReadError,
@@ -42,8 +44,8 @@ async def write(self, buffer: bytes, timeout: float | None = None) -> None:
         if not buffer:
             return
 
-        exc_map: dict[type[Exception], type[Exception]] = {
-            TimeoutError: WriteTimeout,
+        exc_map: ExceptionMapping = {
+            TimeoutError: map_timeout(WriteTimeout),
             anyio.BrokenResourceError: WriteError,
             anyio.ClosedResourceError: WriteError,
         }
@@ -60,8 +62,8 @@ async def start_tls(
         server_hostname: str | None = None,
         timeout: float | None = None,
     ) -> AsyncNetworkStream:
-        exc_map: dict[type[Exception], type[Exception]] = {
-            TimeoutError: ConnectTimeout,
+        exc_map: ExceptionMapping = {
+            TimeoutError: map_timeout(ConnectTimeout),
             anyio.BrokenResourceError: ConnectError,
             anyio.EndOfStream: ConnectError,
             ssl.SSLError: ConnectError,
@@ -107,8 +109,8 @@ async def connect_tcp(
     ) -> AsyncNetworkStream:  # pragma: no cover
         if socket_options is None:
             socket_options = []
-        exc_map: dict[type[Exception], type[Exception]] = {
-            TimeoutError: ConnectTimeout,
+        exc_map: ExceptionMapping = {
+            TimeoutError: map_timeout(ConnectTimeout),
             OSError: ConnectError,
             anyio.BrokenResourceError: ConnectError,
         }
@@ -132,8 +134,8 @@ async def connect_unix_socket(
     ) -> AsyncNetworkStream:  # pragma: no cover
         if socket_options is None:
             socket_options = []
-        exc_map: dict[type[Exception], type[Exception]] = {
-            TimeoutError: ConnectTimeout,
+        exc_map: ExceptionMapping = {
+            TimeoutError: map_timeout(ConnectTimeout),
             OSError: ConnectError,
             anyio.BrokenResourceError: ConnectError,
         }
diff --git a/src/httpcore2/httpcore2/_backends/trio.py b/src/httpcore2/httpcore2/_backends/trio.py
index 742985b9..1e9ebe90 100644
--- a/src/httpcore2/httpcore2/_backends/trio.py
+++ b/src/httpcore2/httpcore2/_backends/trio.py
@@ -14,6 +14,7 @@
     WriteError,
     WriteTimeout,
     map_exceptions,
+    map_timeout,
 )
 from .base import SOCKET_OPTION, AsyncNetworkBackend, AsyncNetworkStream
 
@@ -25,7 +26,7 @@ def __init__(self, stream: trio.abc.Stream) -> None:
     async def read(self, max_bytes: int, timeout: float | None = None) -> bytes:
         timeout_or_inf = float("inf") if timeout is None else timeout
         exc_map: ExceptionMapping = {
-            trio.TooSlowError: ReadTimeout,
+            trio.TooSlowError: map_timeout(ReadTimeout),
             trio.BrokenResourceError: ReadError,
             trio.ClosedResourceError: ReadError,
         }
@@ -40,7 +41,7 @@ async def write(self, buffer: bytes, timeout: float | None = None) -> None:
 
         timeout_or_inf = float("inf") if timeout is None else timeout
         exc_map: ExceptionMapping = {
-            trio.TooSlowError: WriteTimeout,
+            trio.TooSlowError: map_timeout(WriteTimeout),
             trio.BrokenResourceError: WriteError,
             trio.ClosedResourceError: WriteError,
         }
@@ -59,7 +60,7 @@ async def start_tls(
     ) -> AsyncNetworkStream:
         timeout_or_inf = float("inf") if timeout is None else timeout
         exc_map: ExceptionMapping = {
-            trio.TooSlowError: ConnectTimeout,
+            trio.TooSlowError: map_timeout(ConnectTimeout),
             trio.BrokenResourceError: ConnectError,
         }
         ssl_stream = trio.SSLStream(
@@ -121,7 +122,7 @@ async def connect_tcp(
             socket_options = []  # pragma: no cover
         timeout_or_inf = float("inf") if timeout is None else timeout
         exc_map: ExceptionMapping = {
-            trio.TooSlowError: ConnectTimeout,
+            trio.TooSlowError: map_timeout(ConnectTimeout),
             trio.BrokenResourceError: ConnectError,
             OSError: ConnectError,
         }
@@ -142,7 +143,7 @@ async def connect_unix_socket(
             socket_options = []
         timeout_or_inf = float("inf") if timeout is None else timeout
         exc_map: ExceptionMapping = {
-            trio.TooSlowError: ConnectTimeout,
+            trio.TooSlowError: map_timeout(ConnectTimeout),
             trio.BrokenResourceError: ConnectError,
             OSError: ConnectError,
         }
diff --git a/src/httpcore2/httpcore2/_exceptions.py b/src/httpcore2/httpcore2/_exceptions.py
index a54d43b7..61d58133 100644
--- a/src/httpcore2/httpcore2/_exceptions.py
+++ b/src/httpcore2/httpcore2/_exceptions.py
@@ -4,7 +4,7 @@
 import typing
 from collections.abc import Generator
 
-ExceptionMapping = typing.Mapping[type[Exception], type[Exception]]
+ExceptionMapping = typing.Mapping[type[Exception], typing.Callable[[Exception], Exception]]
 
 
 @contextlib.contextmanager
@@ -82,3 +82,10 @@ class ReadError(NetworkError):
 
 class WriteError(NetworkError):
     pass
+
+
+def map_timeout(exception_class: type[TimeoutException]) -> typing.Callable[[Exception], Exception]:
+    def factory(exc: Exception) -> Exception:
+        return exception_class(str(exc) or "timed out")
+
+    return factory
diff --git a/tests/httpx2/test_timeouts.py b/tests/httpx2/test_timeouts.py
index 6ce30e2b..60bef164 100644
--- a/tests/httpx2/test_timeouts.py
+++ b/tests/httpx2/test_timeouts.py
@@ -15,7 +15,7 @@ async def test_read_timeout(server: TestServer) -> None:
     timeout = httpx2.Timeout(None, read=1e-6)
 
     async with httpx2.AsyncClient(timeout=timeout) as client:
-        with pytest.raises(httpx2.ReadTimeout):
+        with pytest.raises(httpx2.ReadTimeout, match="timed out"):
             await client.get(server.url.copy_with(path="/slow_response"))
 
 
@@ -24,7 +24,7 @@ async def test_write_timeout(server: TestServer) -> None:
     timeout = httpx2.Timeout(None, write=1e-6)
 
     async with httpx2.AsyncClient(timeout=timeout) as client:
-        with pytest.raises(httpx2.WriteTimeout):
+        with pytest.raises(httpx2.WriteTimeout, match="timed out"):
             data = b"*" * 1024 * 1024 * 100
             await client.put(server.url.copy_with(path="/slow_response"), content=data)
 
@@ -35,7 +35,7 @@ async def test_connect_timeout(server: TestServer) -> None:
     timeout = httpx2.Timeout(None, connect=1e-6)
 
     async with httpx2.AsyncClient(timeout=timeout) as client:
-        with pytest.raises(httpx2.ConnectTimeout):
+        with pytest.raises(httpx2.ConnectTimeout, match="timed out"):
             # See https://stackoverflow.com/questions/100841/
             await client.get("http://10.255.255.1/")