diff --git a/tests/unit/maxmemory.tcl b/tests/unit/maxmemory.tcl
index 0f64ddc18..3dd706173 100644
--- a/tests/unit/maxmemory.tcl
+++ b/tests/unit/maxmemory.tcl
@@ -144,7 +144,11 @@ start_server {tags {"maxmemory"}} {
 }
 
 proc test_slave_buffers {test_name cmd_count payload_len limit_memory pipeline} {
-    start_server {tags {"maxmemory"}} {
+    # This is a single thread only test because there is a race in getMaxMemoryState
+    #  between zmalloc_used_memory and getting the client outbut buffer memory usage.
+    #  The cure would be worse than the disease, we do not want lock every replica 
+    #  simultaneously just to get more accurate memory usage.
+    start_server {tags {"maxmemory"} overrides { server-threads 1 }} {
         start_server {} {
         set slave_pid [s process_id]
         test "$test_name" {
diff --git a/tests/unit/memefficiency.tcl b/tests/unit/memefficiency.tcl
index 390bad192..0654898ee 100644
--- a/tests/unit/memefficiency.tcl
+++ b/tests/unit/memefficiency.tcl
@@ -37,7 +37,7 @@ start_server {tags {"memefficiency"}} {
 }
 
 run_solo {defrag} {
-start_server {tags {"defrag"}} {
+start_server {tags {"defrag"} overrides {server-threads 1} } {
     if {[string match {*jemalloc*} [s mem_allocator]]} {
         test "Active defrag" {
             r config set save "" ;# prevent bgsave from interfereing with save below
@@ -351,7 +351,7 @@ start_server {tags {"defrag"}} {
             # if the current slab is lower in utilization the defragger would have ended up in stagnation,
             # keept running and not move any allocation.
             # this test is more consistent on a fresh server with no history
-            start_server {tags {"defrag"}} {
+            start_server {tags {"defrag"} overrides {server-threads 1}} {
                 r flushdb
                 r config resetstat
                 r config set save "" ;# prevent bgsave from interfereing with save below