diff --git a/libavutil/rational.c b/libavutil/rational.c
index 4f343f7e32f7bcc03b1d7bb6d4ab467ded2162e6..9fcf621f0ba550566ca2dc078b0fd19188cf294a 100644
--- a/libavutil/rational.c
+++ b/libavutil/rational.c
@@ -51,7 +51,15 @@ int av_reduce(int *dst_nom, int *dst_den, int64_t nom, int64_t den, int64_t max)
         int64_t a2n= x*a1.num + a0.num;
         int64_t a2d= x*a1.den + a0.den;
 
-        if(a2n > max || a2d > max) break;
+        if(a2n > max || a2d > max){
+            if(a1.num) x= (max - a0.num) / a1.num;
+            if(a1.den) x= FFMIN(x, (max - a0.den) / a1.den);
+
+            // Won't overflow, sum == original denominator
+            if (den*(2*x*a1.den + a0.den) > nom*a1.den)
+                a1 = (AVRational){x*a1.num + a0.num, x*a1.den + a0.den};
+            break;
+        }
 
         a0= a1;
         a1= (AVRational){a2n, a2d};