diff --git a/client/editor.js b/client/editor.js
index 8dca1eac..4f953fdf 100644
--- a/client/editor.js
+++ b/client/editor.js
@@ -43,8 +43,10 @@ const forceRefresh = (from_construct_stage) => {
   }
   if (!_.isEqual(output, current)) {
     glyph.stages[stage.type] = output;
-    for (let i = types.indexOf(stage.type) + 1; i < types.length; i++) {
-      glyph.stages[types[i]] = null;
+    if (!output || !current || stage.clearLaterStages(output, current)) {
+      for (let i = types.indexOf(stage.type) + 1; i < types.length; i++) {
+        glyph.stages[types[i]] = null;
+      }
     }
     Session.set('editor.glyph', glyph);
   }
diff --git a/client/lib/abstract.js b/client/lib/abstract.js
index 93587336..b5ecd272 100644
--- a/client/lib/abstract.js
+++ b/client/lib/abstract.js
@@ -38,6 +38,12 @@ stages.AbstractStage = class AbstractStage {
     Session.set('stage.points', undefined);
     Session.set('stage.status', undefined);
   }
+  // Returns true if the difference between the two outputs is significant
+  // enough that the output from all later stages must be erased. By default,
+  // we return true to be safe. We should be very careful when returning false.
+  clearLaterStages(output1, output2) {
+    return true;
+  }
   // Return this stage's value based on current internal state. The default
   // implementation works for stages that follow the 'original/adjusted'
   // convention described in the constructor.
diff --git a/client/lib/analysis.js b/client/lib/analysis.js
index b2a081af..9f03d375 100644
--- a/client/lib/analysis.js
+++ b/client/lib/analysis.js
@@ -130,6 +130,9 @@ stages.analysis = class AnalysisStage extends stages.AbstractStage {
     stage = this;
     updateStatus();
   }
+  clearLaterStages(output1, output2) {
+    return output1.decomposition !== output2.decomposition;
+  }
   getStageOutput() {
     return {
       decomposition: decomposition_util.convertTreeToDecomposition(this.tree),