diff --git a/ssl/ssl_lib.c b/ssl/ssl_lib.c
index c38fc58..1dd355d 100644
--- a/ssl/ssl_lib.c
+++ b/ssl/ssl_lib.c
@@ -3365,13 +3365,33 @@
 
     i = s->session_ctx->session_cache_mode;
     if ((i & mode) != 0
-        && (!s->hit || SSL_IS_TLS13(s))
-        && ((i & SSL_SESS_CACHE_NO_INTERNAL_STORE) != 0
-            || SSL_CTX_add_session(s->session_ctx, s->session))
-        && s->session_ctx->new_session_cb != NULL) {
-        SSL_SESSION_up_ref(s->session);
-        if (!s->session_ctx->new_session_cb(s, s->session))
-            SSL_SESSION_free(s->session);
+        && (!s->hit || SSL_IS_TLS13(s))) {
+        /*
+         * Add the session to the internal cache. In server side TLSv1.3 we
+         * normally don't do this because its a full stateless ticket with only
+         * a dummy session id so there is no reason to cache it, unless:
+         * - we are doing early_data, in which case we cache so that we can
+         *   detect replays
+         * - the application has set a remove_session_cb so needs to know about
+         *   session timeout events
+         */
+        if ((i & SSL_SESS_CACHE_NO_INTERNAL_STORE) == 0
+                && (!SSL_IS_TLS13(s)
+                    || !s->server
+                    || s->max_early_data > 0
+                    || s->session_ctx->remove_session_cb != NULL))
+            SSL_CTX_add_session(s->session_ctx, s->session);
+
+        /*
+         * Add the session to the external cache. We do this even in server side
+         * TLSv1.3 without early data because some applications just want to
+         * know about the creation of a session and aren't doing a full cache.
+         */
+        if (s->session_ctx->new_session_cb != NULL) {
+            SSL_SESSION_up_ref(s->session);
+            if (!s->session_ctx->new_session_cb(s, s->session))
+                SSL_SESSION_free(s->session);
+        }
     }
 
     /* auto flush every 255 connections */
diff --git a/test/sslapitest.c b/test/sslapitest.c
index fe355f2..fe1c1e6 100644
--- a/test/sslapitest.c
+++ b/test/sslapitest.c
@@ -1072,9 +1072,22 @@
             || !TEST_ptr(sess2 = SSL_get1_session(serverssl1)))
         goto end;
 
-    /* Should fail because it should already be in the cache */
-    if (use_int_cache && !TEST_false(SSL_CTX_add_session(sctx, sess2)))
-        goto end;
+    if (use_int_cache) {
+        if (maxprot == TLS1_3_VERSION && !use_ext_cache) {
+            /*
+             * In TLSv1.3 it should not have been added to the internal cache,
+             * except in the case where we also have an external cache (in that
+             * case it gets added to the cache in order to generate remove
+             * events after timeout).
+             */
+            if (!TEST_false(SSL_CTX_remove_session(sctx, sess2)))
+                goto end;
+        } else {
+            /* Should fail because it should already be in the cache */
+            if (!TEST_false(SSL_CTX_add_session(sctx, sess2)))
+                goto end;
+        }
+    }
 
     if (use_ext_cache) {
         SSL_SESSION *tmp = sess2;
@@ -1088,7 +1101,7 @@
          * the external cache. We take a copy first because
          * SSL_CTX_remove_session() also marks the session as non-resumable.
          */
-        if (use_int_cache) {
+        if (use_int_cache && maxprot != TLS1_3_VERSION) {
             if (!TEST_ptr(tmp = SSL_SESSION_dup(sess2))
                     || !TEST_true(SSL_CTX_remove_session(sctx, sess2)))
                 goto end;