diff --git a/libavformat/tls_openssl.c b/libavformat/tls_openssl.c
index c551ac74e2..178ca9e0e4 100644
--- a/libavformat/tls_openssl.c
+++ b/libavformat/tls_openssl.c
@@ -233,12 +233,17 @@ static int tls_open(URLContext *h, const char *uri, int flags, AVDictionary **op
     if ((ret = ff_tls_open_underlying(c, h, uri, options)) < 0)
         goto fail;
 
-    p->ctx = SSL_CTX_new(c->listen ? TLSv1_server_method() : TLSv1_client_method());
+    // We want to support all versions of TLS >= 1.0, but not the deprecated
+    // and insecure SSLv2 and SSLv3.  Despite the name, SSLv23_*_method()
+    // enables support for all versions of SSL and TLS, and we then disable
+    // support for the old protocols immediately after creating the context.
+    p->ctx = SSL_CTX_new(c->listen ? SSLv23_server_method() : SSLv23_client_method());
     if (!p->ctx) {
         av_log(h, AV_LOG_ERROR, "%s\n", ERR_error_string(ERR_get_error(), NULL));
         ret = AVERROR(EIO);
         goto fail;
     }
+    SSL_CTX_set_options(p->ctx, SSL_OP_NO_SSLv2 | SSL_OP_NO_SSLv3);
     if (c->ca_file) {
         if (!SSL_CTX_load_verify_locations(p->ctx, c->ca_file, NULL))
             av_log(h, AV_LOG_ERROR, "SSL_CTX_load_verify_locations %s\n", ERR_error_string(ERR_get_error(), NULL));