diff --git a/hw/core/machine.c b/hw/core/machine.c
index 775add0795..ada300542b 100644
--- a/hw/core/machine.c
+++ b/hw/core/machine.c
@@ -745,11 +745,24 @@ static void smp_parse(MachineState *ms, SMPConfiguration *config, Error **errp)
 {
     unsigned cpus    = config->has_cpus ? config->cpus : 0;
     unsigned sockets = config->has_sockets ? config->sockets : 0;
+    unsigned dies    = config->has_dies ? config->dies : 0;
     unsigned cores   = config->has_cores ? config->cores : 0;
     unsigned threads = config->has_threads ? config->threads : 0;
+    unsigned maxcpus = config->has_maxcpus ? config->maxcpus : 0;
+
+    if ((config->has_cpus && config->cpus == 0) ||
+        (config->has_sockets && config->sockets == 0) ||
+        (config->has_dies && config->dies == 0) ||
+        (config->has_cores && config->cores == 0) ||
+        (config->has_threads && config->threads == 0) ||
+        (config->has_maxcpus && config->maxcpus == 0)) {
+        error_setg(errp, "parameters must be equal to or greater than one if provided");
+        return;
+    }
 
-    if (config->has_dies && config->dies != 0 && config->dies != 1) {
+    if (dies > 1) {
         error_setg(errp, "dies not supported by this machine's CPU topology");
+        return;
     }
 
     /* compute missing values, prefer sockets over cores over threads */
@@ -760,8 +773,8 @@ static void smp_parse(MachineState *ms, SMPConfiguration *config, Error **errp)
             sockets = sockets > 0 ? sockets : 1;
             cpus = cores * threads * sockets;
         } else {
-            ms->smp.max_cpus = config->has_maxcpus ? config->maxcpus : cpus;
-            sockets = ms->smp.max_cpus / (cores * threads);
+            maxcpus = maxcpus > 0 ? maxcpus : cpus;
+            sockets = maxcpus / (cores * threads);
         }
     } else if (cores == 0) {
         threads = threads > 0 ? threads : 1;
@@ -778,26 +791,27 @@ static void smp_parse(MachineState *ms, SMPConfiguration *config, Error **errp)
         return;
     }
 
-    ms->smp.max_cpus = config->has_maxcpus ? config->maxcpus : cpus;
+    maxcpus = maxcpus > 0 ? maxcpus : cpus;
 
-    if (ms->smp.max_cpus < cpus) {
+    if (maxcpus < cpus) {
         error_setg(errp, "maxcpus must be equal to or greater than smp");
         return;
     }
 
-    if (sockets * cores * threads != ms->smp.max_cpus) {
+    if (sockets * cores * threads != maxcpus) {
         error_setg(errp, "Invalid CPU topology: "
                    "sockets (%u) * cores (%u) * threads (%u) "
                    "!= maxcpus (%u)",
                    sockets, cores, threads,
-                   ms->smp.max_cpus);
+                   maxcpus);
         return;
     }
 
     ms->smp.cpus = cpus;
+    ms->smp.sockets = sockets;
     ms->smp.cores = cores;
     ms->smp.threads = threads;
-    ms->smp.sockets = sockets;
+    ms->smp.max_cpus = maxcpus;
 }
 
 static void machine_get_smp(Object *obj, Visitor *v, const char *name,
diff --git a/hw/i386/pc.c b/hw/i386/pc.c
index c2b9d62a35..db93841097 100644
--- a/hw/i386/pc.c
+++ b/hw/i386/pc.c
@@ -716,9 +716,23 @@ static void pc_smp_parse(MachineState *ms, SMPConfiguration *config, Error **err
 {
     unsigned cpus    = config->has_cpus ? config->cpus : 0;
     unsigned sockets = config->has_sockets ? config->sockets : 0;
-    unsigned dies    = config->has_dies ? config->dies : 1;
+    unsigned dies    = config->has_dies ? config->dies : 0;
     unsigned cores   = config->has_cores ? config->cores : 0;
     unsigned threads = config->has_threads ? config->threads : 0;
+    unsigned maxcpus = config->has_maxcpus ? config->maxcpus : 0;
+
+    if ((config->has_cpus && config->cpus == 0) ||
+        (config->has_sockets && config->sockets == 0) ||
+        (config->has_dies && config->dies == 0) ||
+        (config->has_cores && config->cores == 0) ||
+        (config->has_threads && config->threads == 0) ||
+        (config->has_maxcpus && config->maxcpus == 0)) {
+        error_setg(errp, "parameters must be equal to or greater than one if provided");
+        return;
+    }
+
+    /* directly default dies to 1 if it's omitted */
+    dies = dies > 0 ? dies : 1;
 
     /* compute missing values, prefer sockets over cores over threads */
     if (cpus == 0 || sockets == 0) {
@@ -728,8 +742,8 @@ static void pc_smp_parse(MachineState *ms, SMPConfiguration *config, Error **err
             sockets = sockets > 0 ? sockets : 1;
             cpus = cores * threads * dies * sockets;
         } else {
-            ms->smp.max_cpus = config->has_maxcpus ? config->maxcpus : cpus;
-            sockets = ms->smp.max_cpus / (cores * threads * dies);
+            maxcpus = maxcpus > 0 ? maxcpus : cpus;
+            sockets = maxcpus / (cores * threads * dies);
         }
     } else if (cores == 0) {
         threads = threads > 0 ? threads : 1;
@@ -746,27 +760,28 @@ static void pc_smp_parse(MachineState *ms, SMPConfiguration *config, Error **err
         return;
     }
 
-    ms->smp.max_cpus = config->has_maxcpus ? config->maxcpus : cpus;
+    maxcpus = maxcpus > 0 ? maxcpus : cpus;
 
-    if (ms->smp.max_cpus < cpus) {
+    if (maxcpus < cpus) {
         error_setg(errp, "maxcpus must be equal to or greater than smp");
         return;
     }
 
-    if (sockets * dies * cores * threads != ms->smp.max_cpus) {
+    if (sockets * dies * cores * threads != maxcpus) {
         error_setg(errp, "Invalid CPU topology deprecated: "
                    "sockets (%u) * dies (%u) * cores (%u) * threads (%u) "
                    "!= maxcpus (%u)",
                    sockets, dies, cores, threads,
-                   ms->smp.max_cpus);
+                   maxcpus);
         return;
     }
 
     ms->smp.cpus = cpus;
-    ms->smp.cores = cores;
-    ms->smp.threads = threads;
     ms->smp.sockets = sockets;
     ms->smp.dies = dies;
+    ms->smp.cores = cores;
+    ms->smp.threads = threads;
+    ms->smp.max_cpus = maxcpus;
 }
 
 static
diff --git a/qapi/machine.json b/qapi/machine.json
index c3210ee1fb..9272cb3cf8 100644
--- a/qapi/machine.json
+++ b/qapi/machine.json
@@ -1288,8 +1288,8 @@
 ##
 # @SMPConfiguration:
 #
-# Schema for CPU topology configuration.  "0" or a missing value lets
-# QEMU figure out a suitable value based on the ones that are provided.
+# Schema for CPU topology configuration. A missing value lets QEMU
+# figure out a suitable value based on the ones that are provided.
 #
 # @cpus: number of virtual CPUs in the virtual machine
 #
@@ -1297,7 +1297,7 @@
 #
 # @dies: number of dies per socket in the CPU topology
 #
-# @cores: number of cores per thread in the CPU topology
+# @cores: number of cores per die in the CPU topology
 #
 # @threads: number of threads per core in the CPU topology
 #
