diff --git a/docs/middleware.md b/docs/middleware.md
index be4cb23c..a814b7e6 100644
--- a/docs/middleware.md
+++ b/docs/middleware.md
@@ -97,6 +97,25 @@ The following arguments are supported:
 
 If an incoming request does not validate correctly then a 400 response will be sent.
 
+## GZipMiddleware
+
+Handles GZip responses for any request that includes `"gzip"` in the `Accept-Encoding` header.
+
+The middleware will handle both standard and streaming responses.
+
+```python
+from starlette.applications import Starlette
+from starlette.middleware.trustedhost import TrustedHostMiddleware
+
+
+app = Starlette()
+app.add_middleware(GZipMiddleware, minimum_size=1000)
+```
+
+The following arguments are supported:
+
+* `minimum_size` - Do not GZip responses that are smaller than this minimum size in bytes. Defaults to `500`.
+
 ## Using ASGI middleware without Starlette
 
 To wrap ASGI middleware around other ASGI applications, you should use the
diff --git a/starlette/datastructures.py b/starlette/datastructures.py
index 2705fd31..649ff346 100644
--- a/starlette/datastructures.py
+++ b/starlette/datastructures.py
@@ -285,3 +285,9 @@ class MutableHeaders(Headers):
     def update(self, other: dict):
         for key, val in other.items():
             self[key] = val
+
+    def add_vary_header(self, vary):
+        existing = self.get("vary")
+        if existing is not None:
+            vary = ", ".join([existing, vary])
+        self["vary"] = vary
diff --git a/starlette/middleware/cors.py b/starlette/middleware/cors.py
index 8bc33804..8b0abeae 100644
--- a/starlette/middleware/cors.py
+++ b/starlette/middleware/cors.py
@@ -32,8 +32,6 @@ class CORSMiddleware:
         simple_headers = {}
         if "*" in allow_origins:
             simple_headers["Access-Control-Allow-Origin"] = "*"
-        else:
-            simple_headers["Vary"] = "Origin"
         if allow_credentials:
             simple_headers["Access-Control-Allow-Credentials"] = "true"
         if expose_headers:
@@ -142,6 +140,7 @@ class CORSMiddleware:
             await send(message)
             return
 
+        print(message)
         message.setdefault("headers", [])
         headers = MutableHeaders(message["headers"])
         origin = request_headers["Origin"]
@@ -156,7 +155,7 @@ class CORSMiddleware:
         # the Origin header in the response.
         elif not self.allow_all_origins and self.is_allowed_origin(origin=origin):
             headers["Access-Control-Allow-Origin"] = origin
-            if "vary" in headers:
-                self.simple_headers["Vary"] = f"{headers.get('vary')}, Origin"
+            headers.add_vary_header("Origin")
+            print(headers)
         headers.update(self.simple_headers)
         await send(message)
diff --git a/starlette/middleware/gzip.py b/starlette/middleware/gzip.py
new file mode 100644
index 00000000..091c96e3
--- /dev/null
+++ b/starlette/middleware/gzip.py
@@ -0,0 +1,95 @@
+from starlette.datastructures import Headers, MutableHeaders
+from starlette.types import ASGIApp, ASGIInstance, Scope, Receive, Send, Message
+import gzip
+import io
+import typing
+
+
+class GZipMiddleware:
+    def __init__(self, app: ASGIApp, minimum_size: int = 500) -> None:
+        self.app = app
+        self.minimum_size = minimum_size
+
+    def __call__(self, scope: Scope) -> ASGIInstance:
+        if scope["type"] == "http":
+            headers = Headers(scope["headers"])
+            if "gzip" in headers.get("Accept-Encoding", ""):
+                return GZipResponder(self.app, scope, self.minimum_size)
+        return self.app(scope)
+
+
+class GZipResponder:
+    def __init__(self, app: ASGIApp, scope: Scope, minimum_size: int) -> None:
+        self.inner = app(scope)
+        self.minimum_size = minimum_size
+        self.send = unattached_send  # type: Send
+        self.initial_message = {}  # type: Message
+        self.started = False
+        self.gzip_buffer = io.BytesIO()
+        self.gzip_file = gzip.GzipFile(mode="wb", fileobj=self.gzip_buffer)
+
+    async def __call__(self, receive: Receive, send: Send) -> None:
+        self.send = send
+        await self.inner(receive, self.send_with_gzip)
+
+    async def send_with_gzip(self, message: Message) -> None:
+        message_type = message["type"]
+        if message_type == "http.response.start":
+            # Don't send the initial message until we've determined how to
+            # modify the ougoging headers correctly.
+            self.initial_message = message
+        elif message_type == "http.response.body" and not self.started:
+            self.started = True
+            body = message.get("body", b"")
+            more_body = message.get("more_body", False)
+            if len(body) < self.minimum_size and not more_body:
+                # Don't apply GZip to small outgoing responses.
+                await self.send(self.initial_message)
+                await self.send(message)
+            elif not more_body:
+                # Standard GZip response.
+                self.gzip_file.write(body)
+                self.gzip_file.close()
+                body = self.gzip_buffer.getvalue()
+
+                headers = MutableHeaders(self.initial_message["headers"])
+                headers["Content-Encoding"] = "gzip"
+                headers["Content-Length"] = str(len(body))
+                headers.add_vary_header("Accept-Encoding")
+                message["body"] = body
+
+                await self.send(self.initial_message)
+                await self.send(message)
+            else:
+                # Initial body in streaming GZip response.
+                headers = MutableHeaders(self.initial_message["headers"])
+                headers["Content-Encoding"] = "gzip"
+                headers.add_vary_header("Accept-Encoding")
+                del headers["Content-Length"]
+
+                self.gzip_file.write(body)
+                message["body"] = self.gzip_buffer.getvalue()
+                self.gzip_buffer.seek(0)
+                self.gzip_buffer.truncate()
+
+                await self.send(self.initial_message)
+                await self.send(message)
+
+        elif message_type == "http.response.body":
+            # Remaining body in streaming GZip response.
+            body = message.get("body", b"")
+            more_body = message.get("more_body", False)
+
+            self.gzip_file.write(body)
+            if not more_body:
+                self.gzip_file.close()
+
+            message["body"] = self.gzip_buffer.getvalue()
+            self.gzip_buffer.seek(0)
+            self.gzip_buffer.truncate()
+
+            await self.send(message)
+
+
+async def unattached_send(message: Message):
+    raise RuntimeError("send awaitable not set")  # pragma: no cover
diff --git a/tests/test_middleware.py b/tests/middleware/test_cors.py
similarity index 86%
rename from tests/test_middleware.py
rename to tests/middleware/test_cors.py
index ab3a0772..ddd00287 100644
--- a/tests/test_middleware.py
+++ b/tests/middleware/test_cors.py
@@ -1,48 +1,9 @@
 from starlette.applications import Starlette
 from starlette.middleware.cors import CORSMiddleware
-from starlette.middleware.httpsredirect import HTTPSRedirectMiddleware
-from starlette.middleware.trustedhost import TrustedHostMiddleware
 from starlette.responses import PlainTextResponse
 from starlette.testclient import TestClient
 
 
-def test_trusted_host_middleware():
-    app = Starlette()
-
-    app.add_middleware(TrustedHostMiddleware, allowed_hosts=["testserver"])
-
-    @app.route("/")
-    def homepage(request):
-        return PlainTextResponse("OK", status_code=200)
-
-    client = TestClient(app)
-    response = client.get("/")
-    assert response.status_code == 200
-
-    client = TestClient(app, base_url="http://invalidhost")
-    response = client.get("/")
-    assert response.status_code == 400
-
-
-def test_https_redirect_middleware():
-    app = Starlette()
-
-    app.add_middleware(HTTPSRedirectMiddleware)
-
-    @app.route("/")
-    def homepage(request):
-        return PlainTextResponse("OK", status_code=200)
-
-    client = TestClient(app, base_url="https://testserver")
-    response = client.get("/")
-    assert response.status_code == 200
-
-    client = TestClient(app)
-    response = client.get("/", allow_redirects=False)
-    assert response.status_code == 301
-    assert response.headers["location"] == "https://testserver/"
-
-
 def test_cors_allow_all():
     app = Starlette()
 
diff --git a/tests/middleware/test_gzip.py b/tests/middleware/test_gzip.py
new file mode 100644
index 00000000..cd989b8c
--- /dev/null
+++ b/tests/middleware/test_gzip.py
@@ -0,0 +1,77 @@
+from starlette.applications import Starlette
+from starlette.middleware.gzip import GZipMiddleware
+from starlette.responses import PlainTextResponse, StreamingResponse
+from starlette.testclient import TestClient
+
+
+def test_gzip_responses():
+    app = Starlette()
+
+    app.add_middleware(GZipMiddleware)
+
+    @app.route("/")
+    def homepage(request):
+        return PlainTextResponse("x" * 4000, status_code=200)
+
+    client = TestClient(app)
+    response = client.get("/", headers={"accept-encoding": "gzip"})
+    assert response.status_code == 200
+    assert response.text == "x" * 4000
+    assert response.headers["Content-Encoding"] == "gzip"
+    assert int(response.headers["Content-Length"]) < 4000
+
+
+def test_gzip_not_in_accept_encoding():
+    app = Starlette()
+
+    app.add_middleware(GZipMiddleware)
+
+    @app.route("/")
+    def homepage(request):
+        return PlainTextResponse("x" * 4000, status_code=200)
+
+    client = TestClient(app)
+    response = client.get("/", headers={"accept-encoding": "identity"})
+    assert response.status_code == 200
+    assert response.text == "x" * 4000
+    assert "Content-Encoding" not in response.headers
+    assert int(response.headers["Content-Length"]) == 4000
+
+
+def test_gzip_ignored_for_small_responses():
+    app = Starlette()
+
+    app.add_middleware(GZipMiddleware)
+
+    @app.route("/")
+    def homepage(request):
+        return PlainTextResponse("OK", status_code=200)
+
+    client = TestClient(app)
+    response = client.get("/", headers={"accept-encoding": "gzip"})
+    assert response.status_code == 200
+    assert response.text == "OK"
+    assert "Content-Encoding" not in response.headers
+    assert int(response.headers["Content-Length"]) == 2
+
+
+def test_gzip_streaming_response():
+    app = Starlette()
+
+    app.add_middleware(GZipMiddleware)
+
+    @app.route("/")
+    def homepage(request):
+        async def generator(bytes, count):
+            for index in range(count):
+                yield bytes
+
+        streaming = generator(bytes=b"x" * 400, count=10)
+        return StreamingResponse(streaming, status_code=200)
+
+    client = TestClient(app)
+    response = client.get("/", headers={"accept-encoding": "gzip"})
+    assert response.status_code == 200
+    assert response.text == "x" * 4000
+    assert response.headers["Content-Encoding"] == "gzip"
+    assert "Content-Length" not in response.headers
diff --git a/tests/middleware/test_https_redirect.py b/tests/middleware/test_https_redirect.py
new file mode 100644
index 00000000..c36f24e4
--- /dev/null
+++ b/tests/middleware/test_https_redirect.py
@@ -0,0 +1,23 @@
+from starlette.applications import Starlette
+from starlette.middleware.httpsredirect import HTTPSRedirectMiddleware
+from starlette.responses import PlainTextResponse
+from starlette.testclient import TestClient
+
+
+def test_https_redirect_middleware():
+    app = Starlette()
+
+    app.add_middleware(HTTPSRedirectMiddleware)
+
+    @app.route("/")
+    def homepage(request):
+        return PlainTextResponse("OK", status_code=200)
+
+    client = TestClient(app, base_url="https://testserver")
+    response = client.get("/")
+    assert response.status_code == 200
+
+    client = TestClient(app)
+    response = client.get("/", allow_redirects=False)
+    assert response.status_code == 301
+    assert response.headers["location"] == "https://testserver/"
diff --git a/tests/middleware/test_trusted_host.py b/tests/middleware/test_trusted_host.py
new file mode 100644
index 00000000..4b4e86ee
--- /dev/null
+++ b/tests/middleware/test_trusted_host.py
@@ -0,0 +1,22 @@
+from starlette.applications import Starlette
+from starlette.middleware.trustedhost import TrustedHostMiddleware
+from starlette.responses import PlainTextResponse
+from starlette.testclient import TestClient
+
+
+def test_trusted_host_middleware():
+    app = Starlette()
+
+    app.add_middleware(TrustedHostMiddleware, allowed_hosts=["testserver"])
+
+    @app.route("/")
+    def homepage(request):
+        return PlainTextResponse("OK", status_code=200)
+
+    client = TestClient(app)
+    response = client.get("/")
+    assert response.status_code == 200
+
+    client = TestClient(app, base_url="http://invalidhost")
+    response = client.get("/")
+    assert response.status_code == 400