diff --git a/connect.go b/connect.go
index 3149aada..a973e505 100644
--- a/connect.go
+++ b/connect.go
@@ -354,34 +354,87 @@ type handlerConnCloser interface {
 	Close(error) error
 }
 
+// receiveConn represents the shared methods of both StreamingClientConn and StreamingHandlerConn
+// that the below helper functions use for implementing the rules around a "unary" stream, that
+// is expected to have exactly one message (or zero messages followed by a non-EOF error).
+type receiveConn interface {
+	Spec() Spec
+	Receive(any) error
+}
+
+// hasHTTPMethod is implemented by streaming connections that support HTTP methods other than
+// POST.
+type hasHTTPMethod interface {
+	getHTTPMethod() string
+}
+
 // receiveUnaryResponse unmarshals a message from a StreamingClientConn, then
 // envelopes the message and attaches headers and trailers. It attempts to
 // consume the response stream and isn't appropriate when receiving multiple
 // messages.
 func receiveUnaryResponse[T any](conn StreamingClientConn, initializer maybeInitializer) (*Response[T], error) {
+	msg, err := receiveUnaryMessage[T](conn, initializer, "response")
+	if err != nil {
+		return nil, err
+	}
+	return &Response[T]{
+		Msg:     msg,
+		header:  conn.ResponseHeader(),
+		trailer: conn.ResponseTrailer(),
+	}, nil
+}
+
+// receiveUnaryRequest unmarshals a message from a StreamingClientConn, then
+// envelopes the message and attaches headers and other request properties. It
+// attempts to consume the request stream and isn't appropriate when receiving
+// multiple messages.
+func receiveUnaryRequest[T any](conn StreamingHandlerConn, initializer maybeInitializer) (*Request[T], error) {
+	msg, err := receiveUnaryMessage[T](conn, initializer, "request")
+	if err != nil {
+		return nil, err
+	}
+	method := http.MethodPost
+	if hasRequestMethod, ok := conn.(hasHTTPMethod); ok {
+		method = hasRequestMethod.getHTTPMethod()
+	}
+	return &Request[T]{
+		Msg:    msg,
+		spec:   conn.Spec(),
+		peer:   conn.Peer(),
+		header: conn.RequestHeader(),
+		method: method,
+	}, nil
+}
+
+func receiveUnaryMessage[T any](conn receiveConn, initializer maybeInitializer, what string) (*T, error) {
 	var msg T
 	if err := initializer.maybe(conn.Spec(), &msg); err != nil {
 		return nil, err
 	}
+	// Possibly counter-intuitive, but the gRPC specs about error codes state that both clients
+	// and servers should return "unimplemented" when they encounter a cardinality violation: where
+	// the number of messages in the stream is wrong. Search for "cardinality violation" in the
+	// following docs:
+	//    https://grpc.github.io/grpc/core/md_doc_statuscodes.html
 	if err := conn.Receive(&msg); err != nil {
+		if errors.Is(err, io.EOF) {
+			err = NewError(CodeUnimplemented, fmt.Errorf("unary %s has zero messages", what))
+		}
 		return nil, err
 	}
-	// In a well-formed stream, the response message may be followed by a block
-	// of in-stream trailers or HTTP trailers. To ensure that we receive the
-	// trailers, try to read another message from the stream.
-	// TODO: optimise unary calls to avoid this extra receive.
+	// In a well-formed stream, the one message must be the only content in the body.
+	// To verify that it is well-formed, try to read another message from the stream.
+	// TODO: optimise this second receive: ideally do it w/out allocation, w/out
+	//       fully reading next message (if one is present), and w/out trying to
+	//       actually unmarshal the bytes)
 	var msg2 T
 	if err := initializer.maybe(conn.Spec(), &msg2); err != nil {
 		return nil, err
 	}
 	if err := conn.Receive(&msg2); err == nil {
-		return nil, NewError(CodeUnknown, errors.New("unary stream has multiple messages"))
+		return nil, NewError(CodeUnimplemented, fmt.Errorf("unary %s has multiple messages", what))
 	} else if err != nil && !errors.Is(err, io.EOF) {
 		return nil, err
 	}
-	return &Response[T]{
-		Msg:     &msg,
-		header:  conn.ResponseHeader(),
-		trailer: conn.ResponseTrailer(),
-	}, nil
+	return &msg, nil
 }
diff --git a/connect_ext_test.go b/connect_ext_test.go
index 86bdeeff..5f2076d2 100644
--- a/connect_ext_test.go
+++ b/connect_ext_test.go
@@ -1689,6 +1689,7 @@ func TestStreamForServer(t *testing.T) {
 		client := newPingClient(t, &pluggablePingServer{
 			sum: func(ctx context.Context, stream *connect.ClientStream[pingv1.SumRequest]) (*connect.Response[pingv1.SumResponse], error) {
 				assert.True(t, stream.Receive())
+				// We end up sending two response messages, but only one is expected.
 				assert.Nil(t, stream.Conn().Send(&pingv1.SumResponse{Sum: 2}))
 				return connect.NewResponse(&pingv1.SumResponse{}), nil
 			},
@@ -1697,7 +1698,7 @@ func TestStreamForServer(t *testing.T) {
 		assert.Nil(t, stream.Send(&pingv1.SumRequest{Number: 1}))
 		res, err := stream.CloseAndReceive()
 		assert.NotNil(t, err)
-		assert.Equal(t, connect.CodeOf(err), connect.CodeUnknown)
+		assert.Equal(t, connect.CodeOf(err), connect.CodeUnimplemented)
 		assert.Nil(t, res)
 	})
 }
diff --git a/handler.go b/handler.go
index 77724bdf..1d573291 100644
--- a/handler.go
+++ b/handler.go
@@ -63,24 +63,10 @@ func NewUnaryHandler[Req, Res any](
 	}
 	// Given a stream, how should we call the unary function?
 	implementation := func(ctx context.Context, conn StreamingHandlerConn) error {
-		var msg Req
-		if err := config.Initializer.maybe(conn.Spec(), &msg); err != nil {
-			return err
-		}
-		if err := conn.Receive(&msg); err != nil {
+		request, err := receiveUnaryRequest[Req](conn, config.Initializer)
+		if err != nil {
 			return err
 		}
-		method := http.MethodPost
-		if hasRequestMethod, ok := conn.(interface{ getHTTPMethod() string }); ok {
-			method = hasRequestMethod.getHTTPMethod()
-		}
-		request := &Request[Req]{
-			Msg:    &msg,
-			spec:   conn.Spec(),
-			peer:   conn.Peer(),
-			header: conn.RequestHeader(),
-			method: method,
-		}
 		response, err := untyped(ctx, request)
 		if err != nil {
 			return err
@@ -140,24 +126,11 @@ func NewServerStreamHandler[Req, Res any](
 	return newStreamHandler(
 		config,
 		func(ctx context.Context, conn StreamingHandlerConn) error {
-			var msg Req
-			if err := config.Initializer.maybe(conn.Spec(), &msg); err != nil {
-				return err
-			}
-			if err := conn.Receive(&msg); err != nil {
+			req, err := receiveUnaryRequest[Req](conn, config.Initializer)
+			if err != nil {
 				return err
 			}
-			return implementation(
-				ctx,
-				&Request[Req]{
-					Msg:    &msg,
-					spec:   conn.Spec(),
-					peer:   conn.Peer(),
-					header: conn.RequestHeader(),
-					method: http.MethodPost,
-				},
-				&ServerStream[Res]{conn: conn},
-			)
+			return implementation(ctx, req, &ServerStream[Res]{conn: conn})
 		},
 	)
 }
diff --git a/internal/conformance/known-failing.txt b/internal/conformance/known-failing.txt
index 83bcb82f..c92535b2 100644
--- a/internal/conformance/known-failing.txt
+++ b/internal/conformance/known-failing.txt
@@ -25,3 +25,15 @@ HTTP to Connect Code Mapping/**/payload-too-large
 HTTP to Connect Code Mapping/**/precondition-failed
 HTTP to Connect Code Mapping/**/request-header-fields-too-large
 HTTP to Connect Code Mapping/**/request-timeout
+
+# The current v1.0.0-rc3 of conformance suite has expectations for these
+# conditions that were based on the behavior of grpc-go (which returns an
+# "unknown" error), with the incorrect idea that was authoritative (and,
+# honestly, that code makes sense). However, the actual correct behavior,
+# per the specification for gRPC error codes, is for these cardinality
+# violations to instead return "unimplemented":
+#    https://grpc.github.io/grpc/core/md_doc_statuscodes.html
+# This library returns the correct code, which (for now) is interpreted
+# as a failure by the conformance suite.
+**/unary-ok-but-no-response
+**/unary-multiple-responses
\ No newline at end of file