diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index 103809b..0a2ff25 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -130,6 +130,13 @@
     fi
 }
 
+# skip the next test if valgrind is NOT in use
+only_with_valgrind() {
+    if [ "$MEMCHECK" -eq 0 ]; then
+        SKIP_NEXT="YES"
+    fi
+}
+
 # multiply the client timeout delay by the given factor for the next test
 needs_more_time() {
     CLI_DELAY_FACTOR=$1
@@ -2958,13 +2965,22 @@
             -S "The operation timed out" \
             -s "Client initiated reconnection from same port"
 
-run_test    "DTLS client reconnect from same port: reconnect, nbio" \
+not_with_valgrind # server/client too slow to respond in time (next test has higher timeouts)
+run_test    "DTLS client reconnect from same port: reconnect, nbio, no valgrind" \
             "$P_SRV dtls=1 exchanges=2 read_timeout=1000 nbio=2" \
             "$P_CLI dtls=1 exchanges=2 debug_level=2 hs_timeout=500-1000 reconnect_hard=1" \
             0 \
             -S "The operation timed out" \
             -s "Client initiated reconnection from same port"
 
+only_with_valgrind # Only with valgrind, do previous test but with higher read_timeout and hs_timeout
+run_test    "DTLS client reconnect from same port: reconnect, nbio, valgrind" \
+            "$P_SRV dtls=1 exchanges=2 read_timeout=2000 nbio=2 hs_timeout=1500-6000" \
+            "$P_CLI dtls=1 exchanges=2 debug_level=2 hs_timeout=1500-3000 reconnect_hard=1" \
+            0 \
+            -S "The operation timed out" \
+            -s "Client initiated reconnection from same port"
+
 run_test    "DTLS client reconnect from same port: no cookies" \
             "$P_SRV dtls=1 exchanges=2 read_timeout=1000 cookies=0" \
             "$P_CLI dtls=1 exchanges=2 debug_level=2 hs_timeout=500-8000 reconnect_hard=1" \