diff --git a/src/cpu/cpu.c b/src/cpu/cpu.c
index 4a1588d043..580b767b9a 100644
--- a/src/cpu/cpu.c
+++ b/src/cpu/cpu.c
@@ -127,11 +127,13 @@ int
 cpuDecode(virCPUDefPtr cpu,
           const union cpuData *data,
           const char **models,
-          unsigned int nmodels)
+          unsigned int nmodels,
+          const char *preferred)
 {
     struct cpuArchDriver *driver;
 
-    VIR_DEBUG("cpu=%p, data=%p, nmodels=%u", cpu, data, nmodels);
+    VIR_DEBUG("cpu=%p, data=%p, nmodels=%u, preferred=%s",
+              cpu, data, nmodels, NULLSTR(preferred));
     if (models) {
         unsigned int i;
         for (i = 0; i < nmodels; i++)
@@ -160,7 +162,7 @@ cpuDecode(virCPUDefPtr cpu,
         return -1;
     }
 
-    return driver->decode(cpu, data, models, nmodels);
+    return driver->decode(cpu, data, models, nmodels, preferred);
 }
 
 
diff --git a/src/cpu/cpu.h b/src/cpu/cpu.h
index 1494a7f7d4..40f2a7d9cf 100644
--- a/src/cpu/cpu.h
+++ b/src/cpu/cpu.h
@@ -49,7 +49,8 @@ typedef int
 (*cpuArchDecode)    (virCPUDefPtr cpu,
                      const union cpuData *data,
                      const char **models,
-                     unsigned int nmodels);
+                     unsigned int nmodels,
+                     const char *preferred);
 
 typedef int
 (*cpuArchEncode)    (const virCPUDefPtr cpu,
@@ -108,7 +109,8 @@ extern int
 cpuDecode   (virCPUDefPtr cpu,
              const union cpuData *data,
              const char **models,
-             unsigned int nmodels);
+             unsigned int nmodels,
+             const char *preferred);
 
 extern int
 cpuEncode   (const char *arch,
diff --git a/src/cpu/cpu_x86.c b/src/cpu/cpu_x86.c
index b2ca8c831a..633eb69e55 100644
--- a/src/cpu/cpu_x86.c
+++ b/src/cpu/cpu_x86.c
@@ -1064,7 +1064,8 @@ static int
 x86Decode(virCPUDefPtr cpu,
           const union cpuData *data,
           const char **models,
-          unsigned int nmodels)
+          unsigned int nmodels,
+          const char *preferred)
 {
     int ret = -1;
     struct x86_map *map;
@@ -1109,6 +1110,12 @@ x86Decode(virCPUDefPtr cpu,
             }
         }
 
+        if (preferred && STREQ(cpuCandidate->model, preferred)) {
+            virCPUDefFree(cpuModel);
+            cpuModel = cpuCandidate;
+            break;
+        }
+
         if (cpuModel == NULL
             || cpuModel->nfeatures > cpuCandidate->nfeatures) {
             virCPUDefFree(cpuModel);
@@ -1356,7 +1363,7 @@ x86Baseline(virCPUDefPtr *cpus,
     if (!(data = x86DataFromModel(base_model)))
         goto no_memory;
 
-    if (x86Decode(cpu, data, models, nmodels) < 0)
+    if (x86Decode(cpu, data, models, nmodels, NULL) < 0)
         goto error;
 
 cleanup:
diff --git a/src/qemu/qemu_conf.c b/src/qemu/qemu_conf.c
index 262eb5a8e2..2cbcc4fc05 100644
--- a/src/qemu/qemu_conf.c
+++ b/src/qemu/qemu_conf.c
@@ -1029,7 +1029,7 @@ qemudCapsInitCPU(virCapsPtr caps,
     cpu->threads = nodeinfo.threads;
 
     if (!(data = cpuNodeData(arch))
-        || cpuDecode(cpu, data, NULL, 0) < 0)
+        || cpuDecode(cpu, data, NULL, 0, NULL) < 0)
         goto error;
 
     caps->host.cpu = cpu;
@@ -3292,6 +3292,7 @@ qemuBuildCpuArgStr(const struct qemud_driver *driver,
 
     if (ncpus > 0 && host) {
         virCPUCompareResult cmp;
+        const char *preferred;
 
         cmp = cpuGuestData(host, def->cpu, &data);
         switch (cmp) {
@@ -3309,8 +3310,13 @@ qemuBuildCpuArgStr(const struct qemud_driver *driver,
         if (VIR_ALLOC(guest) < 0 || !(guest->arch = strdup(ut->machine)))
             goto no_memory;
 
+        if (def->cpu->match == VIR_CPU_MATCH_MINIMUM)
+            preferred = host->model;
+        else
+            preferred = def->cpu->model;
+
         guest->type = VIR_CPU_TYPE_GUEST;
-        if (cpuDecode(guest, data, cpus, ncpus) < 0)
+        if (cpuDecode(guest, data, cpus, ncpus, preferred) < 0)
             goto cleanup;
 
         virBufferVSprintf(&buf, "%s", guest->model);