diff --git a/httpx/_client.py b/httpx/_client.py
index 1f9f3beb56..5702f490b1 100644
--- a/httpx/_client.py
+++ b/httpx/_client.py
@@ -142,9 +142,8 @@ def __init__(
         self._response = response
         self._timer = timer
 
-    async def __aiter__(self) -> typing.AsyncIterator[bytes]:
-        async for chunk in self._stream:
-            yield chunk
+    def __aiter__(self) -> typing.AsyncIterator[bytes]:
+        return self._stream.__aiter__()
 
     async def aclose(self) -> None:
         seconds = await self._timer.async_elapsed()
diff --git a/httpx/_models.py b/httpx/_models.py
index e0e5278cc0..f6fe5a172f 100644
--- a/httpx/_models.py
+++ b/httpx/_models.py
@@ -4,6 +4,7 @@
 import typing
 import urllib.request
 from collections.abc import Mapping
+from contextlib import aclosing
 from http.cookiejar import Cookie, CookieJar
 
 from ._content import ByteStream, UnattachedStream, encode_request, encode_response
@@ -911,7 +912,7 @@ async def aread(self) -> bytes:
 
     async def aiter_bytes(
         self, chunk_size: typing.Optional[int] = None
-    ) -> typing.AsyncIterator[bytes]:
+    ) -> typing.AsyncGenerator[bytes, None]:
         """
         A byte-iterator over the decoded response content.
         This allows us to handle gzip, deflate, and brotli encoded responses.
@@ -924,19 +925,20 @@ async def aiter_bytes(
             decoder = self._get_content_decoder()
             chunker = ByteChunker(chunk_size=chunk_size)
             with request_context(request=self._request):
-                async for raw_bytes in self.aiter_raw():
-                    decoded = decoder.decode(raw_bytes)
+                async with aclosing(self.aiter_raw()) as stream:
+                    async for raw_bytes in stream:
+                        decoded = decoder.decode(raw_bytes)
+                        for chunk in chunker.decode(decoded):
+                            yield chunk
+                    decoded = decoder.flush()
                     for chunk in chunker.decode(decoded):
+                        yield chunk  # pragma: no cover
+                    for chunk in chunker.flush():
                         yield chunk
-                decoded = decoder.flush()
-                for chunk in chunker.decode(decoded):
-                    yield chunk  # pragma: no cover
-                for chunk in chunker.flush():
-                    yield chunk
 
     async def aiter_text(
         self, chunk_size: typing.Optional[int] = None
-    ) -> typing.AsyncIterator[str]:
+    ) -> typing.AsyncGenerator[str, None]:
         """
         A str-iterator over the decoded response content
         that handles both gzip, deflate, etc but also detects the content's
@@ -945,28 +947,30 @@ async def aiter_text(
         decoder = TextDecoder(encoding=self.encoding or "utf-8")
         chunker = TextChunker(chunk_size=chunk_size)
         with request_context(request=self._request):
-            async for byte_content in self.aiter_bytes():
-                text_content = decoder.decode(byte_content)
+            async with aclosing(self.aiter_bytes()) as stream:
+                async for byte_content in stream:
+                    text_content = decoder.decode(byte_content)
+                    for chunk in chunker.decode(text_content):
+                        yield chunk
+                text_content = decoder.flush()
                 for chunk in chunker.decode(text_content):
                     yield chunk
-            text_content = decoder.flush()
-            for chunk in chunker.decode(text_content):
-                yield chunk
-            for chunk in chunker.flush():
-                yield chunk
+                for chunk in chunker.flush():
+                    yield chunk
 
-    async def aiter_lines(self) -> typing.AsyncIterator[str]:
+    async def aiter_lines(self) -> typing.AsyncGenerator[str, None]:
         decoder = LineDecoder()
         with request_context(request=self._request):
-            async for text in self.aiter_text():
-                for line in decoder.decode(text):
+            async with aclosing(self.aiter_text()) as stream:
+                async for text in stream:
+                    for line in decoder.decode(text):
+                        yield line
+                for line in decoder.flush():
                     yield line
-            for line in decoder.flush():
-                yield line
 
     async def aiter_raw(
         self, chunk_size: typing.Optional[int] = None
-    ) -> typing.AsyncIterator[bytes]:
+    ) -> typing.AsyncGenerator[bytes, None]:
         """
         A byte-iterator over the raw response content.
         """
diff --git a/httpx/_transports/default.py b/httpx/_transports/default.py
index dfd274e7bf..888e28219e 100644
--- a/httpx/_transports/default.py
+++ b/httpx/_transports/default.py
@@ -232,12 +232,14 @@ def close(self) -> None:
 
 class AsyncResponseStream(AsyncByteStream):
     def __init__(self, httpcore_stream: typing.AsyncIterable[bytes]):
-        self._httpcore_stream = httpcore_stream
+        self._httpcore_stream = httpcore_stream.__aiter__()
+
+    def __aiter__(self) -> typing.AsyncIterator[bytes]:
+        return self
 
-    async def __aiter__(self) -> typing.AsyncIterator[bytes]:
+    async def __anext__(self) -> bytes:
         with map_httpcore_exceptions():
-            async for part in self._httpcore_stream:
-                yield part
+            return await self._httpcore_stream.__anext__()
 
     async def aclose(self) -> None:
         if hasattr(self._httpcore_stream, "aclose"):
diff --git a/pyproject.toml b/pyproject.toml
index b11c02825b..b7cc224f78 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -29,7 +29,7 @@ classifiers = [
 ]
 dependencies = [
     "certifi",
-    "httpcore>=0.15.0,<0.17.0",
+    "httpcore==git+https://github.com/encode/httpcore.git@bug/async-early-stream-break",
     "idna",
     "sniffio",
 ]
diff --git a/tests/client/test_async_client.py b/tests/client/test_async_client.py
index 5be0de3b12..2c681b553b 100644
--- a/tests/client/test_async_client.py
+++ b/tests/client/test_async_client.py
@@ -1,4 +1,5 @@
 import typing
+from contextlib import aclosing
 from datetime import timedelta
 
 import pytest
@@ -76,6 +77,34 @@ async def test_stream_response(server):
     assert response.content == b"Hello, world!"
 
 
+@pytest.mark.anyio
+async def test_stream_iterator(server):
+    body = b""
+
+    async with httpx.AsyncClient() as client:
+        async with client.stream("GET", server.url) as response:
+            async for chunk in response.aiter_bytes():
+                body += chunk
+
+    assert response.status_code == 200
+    assert body == b"Hello, world!"
+
+
+@pytest.mark.anyio
+async def test_stream_iterator_partial(server):
+    body = ""
+
+    async with httpx.AsyncClient() as client:
+        async with client.stream("GET", server.url) as response:
+            async with aclosing(response.aiter_text(5)) as stream:
+                async for chunk in stream:
+                    body += chunk
+                    break
+
+    assert response.status_code == 200
+    assert body == "Hello"
+
+
 @pytest.mark.anyio
 async def test_access_content_stream_response(server):
     async with httpx.AsyncClient() as client:
diff --git a/tests/client/test_client.py b/tests/client/test_client.py
index 268cd10689..c35725ecfe 100644
--- a/tests/client/test_client.py
+++ b/tests/client/test_client.py
@@ -107,6 +107,19 @@ def test_stream_iterator(server):
     assert body == b"Hello, world!"
 
 
+def test_stream_iterator_partial(server):
+    body = ""
+
+    with httpx.Client() as client:
+        with client.stream("GET", server.url) as response:
+            for chunk in response.iter_text(5):
+                body += chunk
+                break
+
+    assert response.status_code == 200
+    assert body == "Hello"
+
+
 def test_raw_iterator(server):
     body = b""