diff --git a/crypto/comp/c_zlib.c b/crypto/comp/c_zlib.c
index 7553a2d10..64101bd08 100644
--- a/crypto/comp/c_zlib.c
+++ b/crypto/comp/c_zlib.c
@@ -357,7 +357,17 @@ COMP_METHOD *COMP_zlib(void)
 	if (!zlib_loaded)
 		{
 #if defined(OPENSSL_SYS_WINDOWS) || defined(OPENSSL_SYS_WIN32)
-		zlib_dso = DSO_load(NULL, "ZLIB", NULL, 0);
+		zlib_dso = DSO_load(NULL, "ZLIB1", NULL, 0);
+		if (!zlib_dso)
+			{
+			zlib_dso = DSO_load(NULL, "ZLIB", NULL, 0);
+			if (zlib_dso)
+				{
+				/* Clear the errors from the first failed
+				   DSO_load() */
+				ERR_clear_error();
+				}
+			}
 #else
 		zlib_dso = DSO_load(NULL, "z", NULL, 0);
 #endif