diff --git a/HISTORY.md b/HISTORY.md
index dbdcca824a..efd9844b72 100644
--- a/HISTORY.md
+++ b/HISTORY.md
@@ -1,6 +1,15 @@
 Release History
 ===============
 
+3.2.4 (2023-11-15)
+------------------
+
+**Fixed**
+- Compatibility with some third-party mock tools.
+
+**Changed**
+- Relax IllegalHeader constraint when value is an integer, or float.
+
 3.2.3 (2023-11-11)
 ------------------
 
diff --git a/src/niquests/__version__.py b/src/niquests/__version__.py
index 8eebe9af93..802c034dd0 100644
--- a/src/niquests/__version__.py
+++ b/src/niquests/__version__.py
@@ -9,9 +9,9 @@
 __url__: str = "https://niquests.readthedocs.io"
 
 __version__: str
-__version__ = "3.2.3"
+__version__ = "3.2.4"
 
-__build__: int = 0x030203
+__build__: int = 0x030204
 __author__: str = "Kenneth Reitz"
 __author_email__: str = "me@kennethreitz.org"
 __license__: str = "Apache-2.0"
diff --git a/src/niquests/adapters.py b/src/niquests/adapters.py
index ae4b209ff7..8ec205a74f 100644
--- a/src/niquests/adapters.py
+++ b/src/niquests/adapters.py
@@ -442,7 +442,7 @@ def build_response(
         """
         response = Response()
 
-        if isinstance(resp, BaseHTTPResponse):
+        if isinstance(resp, ResponsePromise) is False:
             # Fallback to None if there's no status_code, for whatever reason.
             response.status_code = getattr(resp, "status", None)
 
@@ -451,8 +451,8 @@ def build_response(
 
             # Set encoding.
             response.encoding = get_encoding_from_headers(response.headers)
-            response.raw = resp
-            response.reason = response.raw.reason
+            response.raw = resp  # type: ignore[assignment]
+            response.reason = response.raw.reason  # type: ignore[union-attr]
 
             if isinstance(req.url, bytes):
                 response.url = req.url.decode("utf-8")
@@ -460,10 +460,10 @@ def build_response(
                 response.url = req.url
 
             # Add new cookies from the server.
-            extract_cookies_to_jar(response.cookies, req, resp)
+            extract_cookies_to_jar(response.cookies, req, resp)  # type: ignore[arg-type]
         else:
             with self._promise_lock:
-                self._promises[resp.uid] = response
+                self._promises[resp.uid] = response  # type: ignore[union-attr]
 
         # Give the Response some context.
         response.request = req
diff --git a/src/niquests/models.py b/src/niquests/models.py
index f9424ca858..8bc8a7c622 100644
--- a/src/niquests/models.py
+++ b/src/niquests/models.py
@@ -832,7 +832,7 @@ class Response:
     server's response to an HTTP request.
     """
 
-    __attrs__ = {
+    __attrs__ = [
         "_content",
         "status_code",
         "headers",
@@ -843,7 +843,7 @@ class Response:
         "cookies",
         "elapsed",
         "request",
-    }
+    ]
 
     __lazy_attrs__ = {
         "json",
@@ -934,7 +934,7 @@ def lazy(self) -> bool:
         Determine if response isn't received and is actually a placeholder.
         Only significant if request was sent through a multiplexed connection.
         """
-        return self.raw is None and hasattr(self, "_gather")
+        return hasattr(self, "raw") and self.raw is None and hasattr(self, "_gather")
 
     def __getattribute__(self, item):
         if item in Response.__lazy_attrs__ and self.lazy:
diff --git a/src/niquests/structures.py b/src/niquests/structures.py
index c975c47101..f3542b696f 100644
--- a/src/niquests/structures.py
+++ b/src/niquests/structures.py
@@ -15,11 +15,24 @@
 from .exceptions import InvalidHeader
 
 
-def _ensure_str_or_bytes(key: typing.Any, value: typing.Any) -> None:
+def _ensure_str_or_bytes(
+    key: typing.Any, value: typing.Any
+) -> tuple[bytes | str, bytes | str]:
+    if isinstance(
+        value,
+        (
+            float,
+            int,
+        ),
+    ):
+        if isinstance(key, bytes):
+            key = key.decode()
+        value = str(value)
     if isinstance(key, (bytes, str)) is False or (
         value is not None and isinstance(value, (bytes, str)) is False
     ):
         raise InvalidHeader(f"Illegal header name or value {key}")
+    return key, value
 
 
 class CaseInsensitiveDict(MutableMapping):
@@ -55,14 +68,15 @@ def __init__(self, data=None, **kwargs) -> None:
         ] = OrderedDict()
         if data is None:
             data = {}
+        normalized_items = []
         for k, v in data.items() if hasattr(data, "items") else data:
-            _ensure_str_or_bytes(k, v)
-        self.update(data, **kwargs)
+            normalized_items.append(_ensure_str_or_bytes(k, v))
+        self.update(normalized_items, **kwargs)
 
     def __setitem__(self, key: str | bytes, value: str | bytes) -> None:
         # Use the lowercased key for lookups, but store the actual
         # key alongside the value.
-        _ensure_str_or_bytes(key, value)
+        key, value = _ensure_str_or_bytes(key, value)
         self._store[key.lower()] = (key, value)
 
     def __getitem__(self, key) -> bytes | str:
diff --git a/tests/test_requests.py b/tests/test_requests.py
index c6ccf104fc..86cf85811d 100644
--- a/tests/test_requests.py
+++ b/tests/test_requests.py
@@ -1666,7 +1666,7 @@ def test_header_validation(self, httpbin):
     @pytest.mark.parametrize(
         "invalid_header, key",
         (
-            ({"foo": 3}, "foo"),
+            ({"foo": ...}, "foo"),
             ({"bar": {"foo": "bar"}}, "bar"),
             ({"baz": ["foo", "bar"]}, "baz"),
         ),