diff --git a/fetch_response.go b/fetch_response.go
index ae91bb9eb..dade1c47d 100644
--- a/fetch_response.go
+++ b/fetch_response.go
@@ -104,15 +104,26 @@ func (b *FetchResponseBlock) decode(pd packetDecoder, version int16) (err error)
 			return err
 		}
 
-		// If we have at least one full records, we skip incomplete ones
-		if partial && len(b.RecordsSet) > 0 {
-			break
+		n, err := records.numRecords()
+		if err != nil {
+			return err
 		}
 
-		b.RecordsSet = append(b.RecordsSet, records)
+		if n > 0 || (partial && len(b.RecordsSet) == 0) {
+			b.RecordsSet = append(b.RecordsSet, records)
+
+			if b.Records == nil {
+				b.Records = records
+			}
+		}
 
-		if b.Records == nil {
-			b.Records = records
+		overflow, err := records.isOverflow()
+		if err != nil {
+			return err
+		}
+
+		if partial || overflow {
+			break
 		}
 	}
 
diff --git a/fetch_response_test.go b/fetch_response_test.go
index 4637cc89e..917027644 100644
--- a/fetch_response_test.go
+++ b/fetch_response_test.go
@@ -197,8 +197,15 @@ func TestOverflowMessageFetchResponse(t *testing.T) {
 	if err != nil {
 		t.Fatalf("Unexpected error: %v", err)
 	}
-	if !partial {
-		t.Error("Overflow messages should be partial.")
+	if partial {
+		t.Error("Decoding detected a partial trailing message where there wasn't one.")
+	}
+	overflow, err := block.Records.isOverflow()
+	if err != nil {
+		t.Fatalf("Unexpected error: %v", err)
+	}
+	if !overflow {
+		t.Error("Decoding detected a partial trailing message where there wasn't one.")
 	}
 
 	n, err := block.Records.numRecords()
diff --git a/message_set.go b/message_set.go
index 27db52fdf..600c7c4df 100644
--- a/message_set.go
+++ b/message_set.go
@@ -47,6 +47,7 @@ func (msb *MessageBlock) decode(pd packetDecoder) (err error) {
 
 type MessageSet struct {
 	PartialTrailingMessage bool // whether the set on the wire contained an incomplete trailing MessageBlock
+	OverflowMessage        bool // whether the set on the wire contained an overflow message
 	Messages               []*MessageBlock
 }
 
@@ -85,7 +86,12 @@ func (ms *MessageSet) decode(pd packetDecoder) (err error) {
 		case ErrInsufficientData:
 			// As an optimization the server is allowed to return a partial message at the
 			// end of the message set. Clients should handle this case. So we just ignore such things.
-			ms.PartialTrailingMessage = true
+			if msb.Offset == -1 {
+				// This is an overflow message caused by chunked down conversion
+				ms.OverflowMessage = true
+			} else {
+				ms.PartialTrailingMessage = true
+			}
 			return nil
 		default:
 			return err
diff --git a/records.go b/records.go
index 301055bb0..192f5927b 100644
--- a/records.go
+++ b/records.go
@@ -163,6 +163,27 @@ func (r *Records) isControl() (bool, error) {
 	return false, fmt.Errorf("unknown records type: %v", r.recordsType)
 }
 
+func (r *Records) isOverflow() (bool, error) {
+	if r.recordsType == unknownRecords {
+		if empty, err := r.setTypeFromFields(); err != nil || empty {
+			return false, err
+		}
+	}
+
+	switch r.recordsType {
+	case unknownRecords:
+		return false, nil
+	case legacyRecords:
+		if r.MsgSet == nil {
+			return false, nil
+		}
+		return r.MsgSet.OverflowMessage, nil
+	case defaultRecords:
+		return false, nil
+	}
+	return false, fmt.Errorf("unknown records type: %v", r.recordsType)
+}
+
 func magicValue(pd packetDecoder) (int8, error) {
 	dec, err := pd.peek(magicOffset, magicLength)
 	if err != nil {