diff --git a/elasticsearch/src/main/java/org/elasticsearch/xpack/prelert/job/persistence/JobResultsPersister.java b/elasticsearch/src/main/java/org/elasticsearch/xpack/prelert/job/persistence/JobResultsPersister.java
index 4881a08b5b3..98fbb3e3f71 100644
--- a/elasticsearch/src/main/java/org/elasticsearch/xpack/prelert/job/persistence/JobResultsPersister.java
+++ b/elasticsearch/src/main/java/org/elasticsearch/xpack/prelert/job/persistence/JobResultsPersister.java
@@ -210,7 +210,7 @@ public class JobResultsPersister extends AbstractComponent {
         String jobId = modelSizeStats.getJobId();
         logger.trace("[{}] Persisting model size stats, for size {}", jobId, modelSizeStats.getModelBytes());
         Persistable persistable = new Persistable(modelSizeStats.getJobId(), modelSizeStats, ModelSizeStats.TYPE::getPreferredName,
-                () -> jobId, () -> toXContentBuilder(modelSizeStats));
+                ModelSizeStats.TYPE::getPreferredName, () -> toXContentBuilder(modelSizeStats));
         persistable.persist();
         persistable = new Persistable(modelSizeStats.getJobId(), modelSizeStats, ModelSizeStats.TYPE::getPreferredName,
                 () -> null, () -> toXContentBuilder(modelSizeStats));
diff --git a/elasticsearch/src/main/java/org/elasticsearch/xpack/prelert/job/process/autodetect/output/AutoDetectResultProcessor.java b/elasticsearch/src/main/java/org/elasticsearch/xpack/prelert/job/process/autodetect/output/AutoDetectResultProcessor.java
index a59cab8efa6..38a58f9ced6 100644
--- a/elasticsearch/src/main/java/org/elasticsearch/xpack/prelert/job/process/autodetect/output/AutoDetectResultProcessor.java
+++ b/elasticsearch/src/main/java/org/elasticsearch/xpack/prelert/job/process/autodetect/output/AutoDetectResultProcessor.java
@@ -126,10 +126,10 @@ public class AutoDetectResultProcessor {
         }
         ModelSizeStats modelSizeStats = result.getModelSizeStats();
         if (modelSizeStats != null) {
-            LOGGER.trace(String.format(Locale.ROOT, "[%s] Parsed ModelSizeStats: %d / %d / %d / %d / %d / %s",
+            LOGGER.trace("[{}] Parsed ModelSizeStats: {} / {} / {} / {} / {} / {}",
                     context.jobId, modelSizeStats.getModelBytes(), modelSizeStats.getTotalByFieldCount(),
                     modelSizeStats.getTotalOverFieldCount(), modelSizeStats.getTotalPartitionFieldCount(),
-                    modelSizeStats.getBucketAllocationFailuresCount(), modelSizeStats.getMemoryStatus()));
+                    modelSizeStats.getBucketAllocationFailuresCount(), modelSizeStats.getMemoryStatus());
 
             latestModelSizeStats = modelSizeStats;
             persister.persistModelSizeStats(modelSizeStats);
diff --git a/elasticsearch/src/test/resources/rest-api-spec/test/jobs_get_stats.yaml b/elasticsearch/src/test/resources/rest-api-spec/test/jobs_get_stats.yaml
index 128c4636f23..c2b2effc81f 100644
--- a/elasticsearch/src/test/resources/rest-api-spec/test/jobs_get_stats.yaml
+++ b/elasticsearch/src/test/resources/rest-api-spec/test/jobs_get_stats.yaml
@@ -40,6 +40,19 @@ setup:
             }
           }
 
+  - do:
+      index:
+        index:  prelertresults-job-stats-test
+        type:   model_size_stats
+        id:     model_size_stats
+        body:   {
+                  "job_id": "job-stats-test",
+                  "log_time": 1480896000000,
+                  "timestamp": 1480896000000,
+                  "model_bytes": 100,
+                  "total_by_field_count": 2
+                }
+
 ---
 "Test get job stats after uploading data prompting the creation of some stats":
   - do:
@@ -70,13 +83,12 @@ setup:
         job_id: job-stats-test
         metric: data_counts
 
+  - match: { jobs.0.job_id : job-stats-test }
   - match: { jobs.0.data_counts.processed_record_count: 2 }
   - match: { jobs.0.data_counts.processed_field_count: 4}
   - match: { jobs.0.data_counts.input_field_count: 4 }
 
 # Test filters
-# It's difficult to test for the presence of model_size_stats as they
-# won't be created with such a small data sample
   - do:
       xpack.prelert.get_jobs:
         job_id: "job-stats-test"
@@ -93,6 +105,7 @@ setup:
   - is_false: jobs.0.config
   - is_false: jobs.0.data_counts
   - is_false: jobs.0.scheduler_state
+  - match: { jobs.0.model_size_stats.model_bytes: 100 }
 
   - do:
       xpack.prelert.get_jobs:
@@ -118,6 +131,7 @@ setup:
   - is_true: jobs.0.config
   - is_true: jobs.0.data_counts
   - is_false: jobs.0.scheduler_state
+  - match: { jobs.0.job_id: job-stats-test }
   - match: { jobs.0.status: RUNNING }
 
   - do: