diff --git a/pkt-line.c b/pkt-line.c
index 844c253ccd..657a702927 100644
--- a/pkt-line.c
+++ b/pkt-line.c
@@ -471,6 +471,9 @@ int recv_sideband(const char *me, int in_stream, int out)
 			write_or_die(out, buf + 1, len - 1);
 			break;
 		default: /* errors: message already written */
+			if (scratch.len > 0)
+				BUG("unhandled incomplete sideband: '%s'",
+				    scratch.buf);
 			return sideband_type;
 		}
 	}
diff --git a/sideband.c b/sideband.c
index 0a60662fa6..a5405b9aaa 100644
--- a/sideband.c
+++ b/sideband.c
@@ -190,7 +190,7 @@ int demultiplex_sideband(const char *me, char *buf, int len,
 		return 0;
 	case 1:
 		*sideband_type = SIDEBAND_PRIMARY;
-		break;
+		return 1;
 	default:
 		strbuf_addf(scratch, "%s%s: protocol error: bad band #%d",
 			    scratch->len ? "\n" : "", me, band);
diff --git a/t/helper/test-pkt-line.c b/t/helper/test-pkt-line.c
index 69152958e5..5e638f0b97 100644
--- a/t/helper/test-pkt-line.c
+++ b/t/helper/test-pkt-line.c
@@ -84,6 +84,25 @@ static void unpack_sideband(void)
 	}
 }
 
+static int send_split_sideband(void)
+{
+	const char *part1 = "Hello,";
+	const char *primary = "\001primary: regular output\n";
+	const char *part2 = " world!\n";
+
+	send_sideband(1, 2, part1, strlen(part1), LARGE_PACKET_MAX);
+	packet_write(1, primary, strlen(primary));
+	send_sideband(1, 2, part2, strlen(part2), LARGE_PACKET_MAX);
+	packet_response_end(1);
+
+	return 0;
+}
+
+static int receive_sideband(void)
+{
+	return recv_sideband("sideband", 0, 1);
+}
+
 int cmd__pkt_line(int argc, const char **argv)
 {
 	if (argc < 2)
@@ -95,6 +114,10 @@ int cmd__pkt_line(int argc, const char **argv)
 		unpack();
 	else if (!strcmp(argv[1], "unpack-sideband"))
 		unpack_sideband();
+	else if (!strcmp(argv[1], "send-split-sideband"))
+		send_split_sideband();
+	else if (!strcmp(argv[1], "receive-sideband"))
+		receive_sideband();
 	else
 		die("invalid argument '%s'", argv[1]);
 
diff --git a/t/t0070-fundamental.sh b/t/t0070-fundamental.sh
index 7b111a56fd..357201640a 100755
--- a/t/t0070-fundamental.sh
+++ b/t/t0070-fundamental.sh
@@ -34,4 +34,10 @@ test_expect_success 'check for a bug in the regex routines' '
 	test-tool regex --bug
 '
 
+test_expect_success 'incomplete sideband messages are reassembled' '
+	test-tool pkt-line send-split-sideband >split-sideband &&
+	test-tool pkt-line receive-sideband <split-sideband 2>err &&
+	grep "Hello, world" err
+'
+
 test_done