diff --git a/script/valgrind.supp b/script/valgrind.supp
index 8459a71ad..d938aa9c9 100644
--- a/script/valgrind.supp
+++ b/script/valgrind.supp
@@ -123,6 +123,26 @@
 	...
 }
 
+{
+	ignore-openssl-undefined-in-read
+	Memcheck:Cond
+	...
+	obj:*libssl.so*
+	...
+	fun:openssl_read
+	...
+}
+
+{
+	ignore-openssl-undefined-in-connect
+	Memcheck:Cond
+	...
+	obj:*libssl.so*
+	...
+	fun:openssl_connect
+	...
+}
+
 {
 	ignore-libssh2-rsa-sha1-sign
 	Memcheck:Leak
diff --git a/src/streams/openssl.c b/src/streams/openssl.c
index fe5f79cce..8613f70be 100644
--- a/src/streams/openssl.c
+++ b/src/streams/openssl.c
@@ -597,6 +597,10 @@ static int openssl_connect(git_stream *stream)
 
 	st->connected = true;
 
+#ifdef VALGRIND
+	VALGRIND_MAKE_MEM_DEFINED(st->ssl, sizeof(SSL));
+#endif
+
 	return verify_server_cert(st->ssl, st->host);
 }