diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index ba6e578c1..6387af573 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -2869,26 +2869,38 @@ run_test    "DTLS cookie: enabled, nbio" \
 
 # Tests for client reconnecting from the same port with DTLS
 
+not_with_valgrind # spurious resend
 run_test    "DTLS client reconnect from same port: reference" \
-            "$P_SRV dtls=1 exchanges=2" \
-            "$P_CLI dtls=1 exchanges=2 debug_level=2" \
+            "$P_SRV dtls=1 exchanges=2 read_timeout=1000" \
+            "$P_CLI dtls=1 exchanges=2 debug_level=2 hs_timeout=500-1000" \
             0 \
             -C "resend" \
+            -S "The operation timed out" \
             -S "Client initiated reconnection from same port"
 
+not_with_valgrind # spurious resend
 run_test    "DTLS client reconnect from same port: reconnect" \
-            "$P_SRV dtls=1 exchanges=2" \
-            "$P_CLI dtls=1 exchanges=2 debug_level=2 reconnect_hard=1" \
+            "$P_SRV dtls=1 exchanges=2 read_timeout=1000" \
+            "$P_CLI dtls=1 exchanges=2 debug_level=2 hs_timeout=500-1000 reconnect_hard=1" \
             0 \
             -C "resend" \
+            -S "The operation timed out" \
             -s "Client initiated reconnection from same port"
 
 run_test    "DTLS client reconnect from same port: reconnect, nbio" \
-            "$P_SRV dtls=1 exchanges=2 nbio=2" \
-            "$P_CLI dtls=1 exchanges=2 debug_level=2 reconnect_hard=1" \
+            "$P_SRV dtls=1 exchanges=2 read_timeout=1000 nbio=2" \
+            "$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"
 
+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=500-1000 reconnect_hard=1" \
+            1 \
+            -s "The operation timed out" \
+            -S "Client initiated reconnection from same port"
+
 # Tests for various cases of client authentication with DTLS
 # (focused on handshake flows and message parsing)