diff --git a/httpx/_models.py b/httpx/_models.py
index 7a3b5885..84739f74 100644
--- a/httpx/_models.py
+++ b/httpx/_models.py
@@ -3,7 +3,7 @@ import email.message
 import json as jsonlib
 import typing
 import urllib.request
-from collections.abc import MutableMapping
+from collections.abc import Mapping, MutableMapping
 from http.cookiejar import Cookie, CookieJar
 
 from ._content import ByteStream, UnattachedStream, encode_request, encode_response
@@ -65,7 +65,7 @@ class Headers(typing.MutableMapping[str, str]):
             self._list = []  # type: typing.List[typing.Tuple[bytes, bytes, bytes]]
         elif isinstance(headers, Headers):
             self._list = list(headers._list)
-        elif isinstance(headers, dict):
+        elif isinstance(headers, Mapping):
             self._list = [
                 (
                     normalize_header_key(k, lower=False, encoding=encoding),
diff --git a/httpx/_types.py b/httpx/_types.py
index 784848ef..8a50314b 100644
--- a/httpx/_types.py
+++ b/httpx/_types.py
@@ -43,8 +43,8 @@ QueryParamTypes = Union[
 
 HeaderTypes = Union[
     "Headers",
-    Dict[str, str],
-    Dict[bytes, bytes],
+    Mapping[str, str],
+    Mapping[bytes, bytes],
     Sequence[Tuple[str, str]],
     Sequence[Tuple[bytes, bytes]],
 ]