diff --git a/configure.ac b/configure.ac
index 2cbd2f53..2b928842 100644
--- a/configure.ac
+++ b/configure.ac
@@ -1084,7 +1084,7 @@ if test x"$with_tiff" != x"no"; then
   )
 fi
 
-# WEBP in TIFF added in libtiff 4.0.10
+# ZSTD and WEBP in TIFF added in libtiff 4.0.10
 if test x"$with_tiff" != x"no"; then
   save_INCLUDES="$INCLUDES"
   INCLUDES="$INCLUDES $TIFF_INCLUDES"
diff --git a/libvips/foreign/vips2tiff.c b/libvips/foreign/vips2tiff.c
index 6c8d6d71..626b36ba 100644
--- a/libvips/foreign/vips2tiff.c
+++ b/libvips/foreign/vips2tiff.c
@@ -659,12 +659,15 @@ wtiff_write_header( Wtiff *wtiff, Layer *layer )
 		TIFFSetField( tif, TIFFTAG_WEBP_LEVEL, wtiff->Q );
 		TIFFSetField( tif, TIFFTAG_WEBP_LOSSLESS, wtiff->lossless );
 	}
-	if( wtiff->compression == COMPRESSION_ZSTD ) 
+	if( wtiff->compression == COMPRESSION_ZSTD ) {
 		TIFFSetField( tif, TIFFTAG_ZSTD_LEVEL, wtiff->level );
+		if( wtiff->predictor != VIPS_FOREIGN_TIFF_PREDICTOR_NONE ) 
+			TIFFSetField( tif, 
+				TIFFTAG_PREDICTOR, wtiff->predictor );
+	}
 #endif /*HAVE_TIFF_COMPRESSION_WEBP*/
 
 	if( (wtiff->compression == COMPRESSION_ADOBE_DEFLATE ||
-		wtiff->compression == COMPRESSION_ZSTD ||
 		wtiff->compression == COMPRESSION_LZW) &&
 		wtiff->predictor != VIPS_FOREIGN_TIFF_PREDICTOR_NONE ) 
 		TIFFSetField( tif, TIFFTAG_PREDICTOR, wtiff->predictor );
@@ -1863,12 +1866,15 @@ wtiff_copy_tiff( Wtiff *wtiff, TIFF *out, TIFF *in )
 		TIFFSetField( out, TIFFTAG_WEBP_LEVEL, wtiff->Q );
 		TIFFSetField( out, TIFFTAG_WEBP_LOSSLESS, wtiff->lossless );
 	}
-	if( wtiff->compression == COMPRESSION_ZSTD ) 
+	if( wtiff->compression == COMPRESSION_ZSTD ) {
 		TIFFSetField( out, TIFFTAG_ZSTD_LEVEL, wtiff->level );
+		if( wtiff->predictor != VIPS_FOREIGN_TIFF_PREDICTOR_NONE ) 
+			TIFFSetField( out, 
+				TIFFTAG_PREDICTOR, wtiff->predictor );
+	}
 #endif /*HAVE_TIFF_COMPRESSION_WEBP*/
 
 	if( (wtiff->compression == COMPRESSION_ADOBE_DEFLATE ||
-		wtiff->compression == COMPRESSION_ZSTD ||
 		wtiff->compression == COMPRESSION_LZW) &&
 		wtiff->predictor != VIPS_FOREIGN_TIFF_PREDICTOR_NONE ) 
 		TIFFSetField( out, TIFFTAG_PREDICTOR, wtiff->predictor );