diff --git a/libvips/conversion/unpremultiply.c b/libvips/conversion/unpremultiply.c
index efc90b53..219fac28 100644
--- a/libvips/conversion/unpremultiply.c
+++ b/libvips/conversion/unpremultiply.c
@@ -78,17 +78,17 @@ G_DEFINE_TYPE( VipsUnpremultiply, vips_unpremultiply, VIPS_TYPE_CONVERSION );
 	\
 	for( x = 0; x < width; x++ ) { \
 		IN alpha = p[alpha_band]; \
-		IN clip_alpha = VIPS_CLIP( 0, alpha, max_alpha ); \
-		OUT nalpha = (OUT) clip_alpha / max_alpha; \
 		\
-		if( nalpha == 0 ) \
+		if( alpha != 0 ) { \
+			OUT factor = max_alpha / alpha; \
+			\
+			for( i = 0; i < alpha_band; i++ ) \
+				q[i] = factor * p[i]; \
+			q[alpha_band] = alpha; \
+		} \
+		else \
 			for( i = 0; i < alpha_band + 1; i++ ) \
 				q[i] = 0; \
-		else { \
-			for( i = 0; i < alpha_band; i++ ) \
-				q[i] = p[i] / nalpha; \
-			q[alpha_band] = clip_alpha; \
-		} \
 		\
 		for( i = alpha_band + 1; i < bands; i++ ) \
 			q[i] = p[i]; \
@@ -106,21 +106,21 @@ G_DEFINE_TYPE( VipsUnpremultiply, vips_unpremultiply, VIPS_TYPE_CONVERSION );
 	\
 	for( x = 0; x < width; x++ ) { \
 		IN alpha = p[3]; \
-		IN clip_alpha = VIPS_CLIP( 0, alpha, max_alpha ); \
-		OUT nalpha = (OUT) clip_alpha / max_alpha; \
 		\
-		if( nalpha == 0 ) { \
+		if( alpha != 0 ) { \
+			OUT factor = max_alpha / alpha; \
+			\
+			q[0] = factor * p[0]; \
+			q[1] = factor * p[1]; \
+			q[2] = factor * p[2]; \
+			q[3] = alpha; \
+		} \
+		else { \
 			q[0] = 0; \
 			q[1] = 0; \
 			q[2] = 0; \
 			q[3] = 0; \
 		} \
-		else { \
-			q[0] = p[0] / nalpha; \
-			q[1] = p[1] / nalpha; \
-			q[2] = p[2] / nalpha; \
-			q[3] = clip_alpha; \
-		} \
 		\
 		p += 4; \
 		q += 4; \