diff --git a/host/include/i386/host/bufferiszero.c.inc b/host/include/i386/host/bufferiszero.c.inc
index 3b9605d806..74ae98580f 100644
--- a/host/include/i386/host/bufferiszero.c.inc
+++ b/host/include/i386/host/bufferiszero.c.inc
@@ -110,13 +110,14 @@ static biz_accel_fn const accel_table[] = {
 
 static unsigned best_accel(void)
 {
-#ifdef CONFIG_AVX2_OPT
     unsigned info = cpuinfo_init();
+
+#ifdef CONFIG_AVX2_OPT
     if (info & CPUINFO_AVX2) {
         return 2;
     }
 #endif
-    return 1;
+    return info & CPUINFO_SSE2 ? 1 : 0;
 }
 
 #else
diff --git a/host/include/i386/host/cpuinfo.h b/host/include/i386/host/cpuinfo.h
index 72f6fad61e..81771733ea 100644
--- a/host/include/i386/host/cpuinfo.h
+++ b/host/include/i386/host/cpuinfo.h
@@ -14,6 +14,7 @@
 #define CPUINFO_POPCNT          (1u << 4)
 #define CPUINFO_BMI1            (1u << 5)
 #define CPUINFO_BMI2            (1u << 6)
+#define CPUINFO_SSE2            (1u << 7)
 #define CPUINFO_AVX1            (1u << 9)
 #define CPUINFO_AVX2            (1u << 10)
 #define CPUINFO_AVX512F         (1u << 11)
diff --git a/util/cpuinfo-i386.c b/util/cpuinfo-i386.c
index ca74ef04f5..90f92a42dc 100644
--- a/util/cpuinfo-i386.c
+++ b/util/cpuinfo-i386.c
@@ -34,6 +34,7 @@ unsigned __attribute__((constructor)) cpuinfo_init(void)
     if (max >= 1) {
         __cpuid(1, a, b, c, d);
 
+        info |= (d & bit_SSE2 ? CPUINFO_SSE2 : 0);
         info |= (c & bit_MOVBE ? CPUINFO_MOVBE : 0);
         info |= (c & bit_POPCNT ? CPUINFO_POPCNT : 0);
         info |= (c & bit_PCLMUL ? CPUINFO_PCLMUL : 0);