diff --git a/main/channel.c b/main/channel.c
index bd157acfa5..6073bf91c7 100644
--- a/main/channel.c
+++ b/main/channel.c
@@ -2068,10 +2068,15 @@ struct ast_channel *ast_waitfor_nandfds(struct ast_channel **c, int n, int *fds,
 	}
 	/* Wait full interval */
 	rms = *ms;
-	if (!ast_tvzero(whentohangup)) {
+	/* INT_MAX, not LONG_MAX, because it matters on 64-bit */
+	if (!ast_tvzero(whentohangup) && whentohangup.tv_sec < INT_MAX / 1000) {
 		rms = whentohangup.tv_sec * 1000 + whentohangup.tv_usec / 1000;              /* timeout in milliseconds */
-		if (*ms >= 0 && *ms < rms)		/* original *ms still smaller */
+		if (*ms >= 0 && *ms < rms) {                                                 /* original *ms still smaller */
 			rms =  *ms;
+		}
+	} else if (!ast_tvzero(whentohangup) && rms < 0) {
+		/* Tiny corner case... call would need to last >24 days */
+		rms = INT_MAX;
 	}
 	/*
 	 * Build the pollfd array, putting the channels' fds first,