diff --git a/internal/conformance/known-failing.txt b/internal/conformance/known-failing.txt
new file mode 100644
index 00000000..8acce3f9
--- /dev/null
+++ b/internal/conformance/known-failing.txt
@@ -0,0 +1,14 @@
+# The current v1.0.0-rc3 of conformance suite wants to see "unknown"
+# as the status for Connect unary responses where the JSON error body
+# is missing the 'code' property. But we instead want clients to
+# synthesize an error code from the HTTP status code. That way, if
+# a proxy or middle-box happens to reply with a JSON error, but not
+# a valid *Connect* error, we can use the HTTP status to derive an
+# error code, just like we do when the response has an unexpected
+# content type.
+#
+# So after we fix the tests in the conformance suite, we can remove
+# these lines below.
+Connect Error and End-Stream/**/error/missing-code
+Connect Error and End-Stream/**/error/null
+Connect Error and End-Stream/**/error/null-code
\ No newline at end of file
diff --git a/internal/conformance/runconformance.sh b/internal/conformance/runconformance.sh
index db4a5f5b..d6de5f4d 100755
--- a/internal/conformance/runconformance.sh
+++ b/internal/conformance/runconformance.sh
@@ -15,7 +15,7 @@ $GO build -o $BINDIR/referenceclient connectrpc.com/conformance/cmd/referencecli
 $GO build -o $BINDIR/referenceserver connectrpc.com/conformance/cmd/referenceserver
 
 echo "Running conformance tests against client..."
-$BINDIR/connectconformance --mode client --conf config.yaml -v --trace -- $BINDIR/referenceclient
+$BINDIR/connectconformance --mode client --conf config.yaml --known-failing @known-failing.txt -v --trace -- $BINDIR/referenceclient
 
 echo "Running conformance tests against server..."
 $BINDIR/connectconformance --mode server --conf config.yaml -v --trace -- $BINDIR/referenceserver
diff --git a/protocol_connect.go b/protocol_connect.go
index e0736442..f07d3002 100644
--- a/protocol_connect.go
+++ b/protocol_connect.go
@@ -547,6 +547,10 @@ func (cc *connectUnaryClientConn) validateResponse(response *http.Response) *Err
 				errors.New(response.Status),
 			)
 		}
+		if wireErr.Code == 0 {
+			// code not set? default to one implied by HTTP status
+			wireErr.Code = connectHTTPToCode(response.StatusCode)
+		}
 		serverErr := wireErr.asError()
 		if serverErr == nil {
 			return nil
@@ -1233,6 +1237,26 @@ func (e *connectWireError) asError() *Error {
 	return err
 }
 
+func (e *connectWireError) UnmarshalJSON(data []byte) error {
+	// We want to be lenient if the JSON has an unrecognized or invalid code.
+	// So if that occurs, we leave the code unset but can still de-serialize
+	// the other fields from the input JSON.
+	var wireError struct {
+		Code    string               `json:"code"`
+		Message string               `json:"message"`
+		Details []*connectWireDetail `json:"details"`
+	}
+	err := json.Unmarshal(data, &wireError)
+	if err != nil {
+		return err
+	}
+	e.Message = wireError.Message
+	e.Details = wireError.Details
+	// This will leave e.Code unset if we can't unmarshal the given string.
+	_ = e.Code.UnmarshalText([]byte(wireError.Code))
+	return nil
+}
+
 type connectEndStreamMessage struct {
 	Error   *connectWireError `json:"error,omitempty"`
 	Trailer http.Header       `json:"metadata,omitempty"`