diff --git a/client/editor.js b/client/editor.js
index cd5ef474..b86acfee 100644
--- a/client/editor.js
+++ b/client/editor.js
@@ -14,6 +14,14 @@ const changeGlyph = (method, argument) => {
   });
 }
 
+const constructStage = (type) => {
+  const glyph = Session.get('editor.glyph');
+  stage = new stages[type](glyph);
+  Session.set('editor.glyph', glyph);
+  stage._type = type;
+  stage.refresh(glyph);
+}
+
 this.getGlyph = (selector) => changeGlyph('getGlyph', selector);
 
 const incrementStage = (amount) => {
@@ -21,10 +29,7 @@ const incrementStage = (amount) => {
   if (index < 0) return;
   const new_index = index + amount;
   if (new_index < 0 || new_index >= types.length) return;
-  const glyph = Session.get('editor.glyph');
-  stage = new stages[types[new_index]](glyph);
-  stage._type = types[new_index];
-  stage.refresh(glyph);
+  constructStage(types[new_index]);
 }
 
 const initialize = () => {
@@ -46,7 +51,9 @@ const bindings = {
 Template.editor.events({
   'click svg .selectable': function(event) {
     // We avoid the arrow function here so that this is bound to the template.
-    stage.handleEvent(Session.get('editor.glyph'), event, this);
+    const glyph = Session.get('editor.glyph');
+    stage.handleEvent(glyph, event, this);
+    Session.set('editor.glyph', glyph);
   }
 });
 
@@ -69,8 +76,7 @@ Tracker.autorun(() => {
   if (!last_glyph || glyph.character !== last_glyph.character) {
     let last_completed_stage = types[0];
     types.map((x) => { if (glyph.stages[x]) last_completed_stage = x; });
-    stage = new stages[last_completed_stage](glyph);
-    stage._type = last_completed_stage;
+    constructStage(last_completed_stage);
   }
   stage.refresh(glyph);
   last_glyph = glyph;
diff --git a/client/lib/abstract.js b/client/lib/abstract.js
index d9735150..27b913d3 100644
--- a/client/lib/abstract.js
+++ b/client/lib/abstract.js
@@ -2,10 +2,11 @@ if (this.stages !== undefined) throw new Error('Redifining stages global!');
 this.stages = {};
 
 stages.AbstractStage = class AbstractStage {
-  // Initialize this stage's internal state. The glyph may already include
-  // output from this stage. If the internal state can be initialized in such
-  // a way to achieve that output, it should be; doing so allows users to make
-  // some edits, switch to another glyph, and later resume where they left off.
+  // This method should fill in this stage's field in glyph.stages. The glyph
+  // may already have a value for this stage set. If so, this stage's internal
+  // state should be initialized in such a way to achieve that output, if that
+  // is possible; doing so allows users to make some edits, switch to another
+  // glyph, and then switch back and continue where they left off.
   constructor(glyph) {
     // Session variables the interface by which the stage interacts with UI:
     //   - type - String type of this stage.
@@ -27,8 +28,8 @@ stages.AbstractStage = class AbstractStage {
     this.colors = ['#0074D9', '#2ECC40', '#FFDC00', '#FF4136', '#7FDBFF',
                    '#001F3F', '#39CCCC', '#3D9970', '#01FF70', '#FF851B'];
   }
-  // Update the stage's internal state and the editor.glyph Session variable
-  // based on the event.
+  // Update the stage's internal state and possibly update this stage's field
+  // in glyph.stages based on the event.
   handleEvent(glyph, event, template) {
     assert(false, 'handleEvent was not implemented!');
   }
diff --git a/client/lib/bridges.js b/client/lib/bridges.js
index afdbbf30..def4d154 100644
--- a/client/lib/bridges.js
+++ b/client/lib/bridges.js
@@ -17,17 +17,16 @@ stages.bridges = class BridgesStage extends stages.AbstractStage {
                 'Connect each pair of points on the glyph outline such that ' +
                 'the segment connecting those points is part of some stroke ' +
                 'outline. Click on a bridge to drop it.');
-    const bridges = stroke_extractor.getBridges(glyph);
+    const bridges = stroke_extractor.getBridges(glyph.stages.path);
     this.bridges = bridges.bridges;
     this.endpoints = [];
     bridges.endpoints.map(
         (path) => this.endpoints = this.endpoints.concat(path));
     this.selected_point = undefined;
-    glyph.stages.strokes = glyph.stages.strokes || this.bridges;
+    glyph.stages.bridges = glyph.stages.bridges || this.bridges;
   }
   handleClickOnBridge(glyph, bridge) {
     glyph.stages.bridges = removeBridge(glyph.stages.bridges, bridge);
-    Session.set('editor.glyph', glyph);
   }
   handleClickOnPoint(glyph, point) {
     if (this.selected_point === undefined) {
@@ -47,7 +46,6 @@ stages.bridges = class BridgesStage extends stages.AbstractStage {
       return;
     }
     glyph.stages.bridges.push(bridge);
-    Session.set('editor.glyph', glyph);
   }
   handleEvent(glyph, event, template) {
     if (template.x1 !== undefined) {
@@ -87,7 +85,8 @@ stages.bridges = class BridgesStage extends stages.AbstractStage {
         stroke: color,
       }
     }));
-    const strokes = stroke_extractor.getStrokes(glyph);
+    const strokes = stroke_extractor.getStrokes(
+        glyph.stages.path, glyph.stages.bridges);
     const n = strokes.strokes.length;
     const message = `Extracted ${n} stroke${n == 1 ? '' : 's'}.`;
     Session.set('stage.status', strokes.log.concat([{message: message}]));
diff --git a/client/lib/strokes.js b/client/lib/strokes.js
index 84025b3c..da56aaf6 100644
--- a/client/lib/strokes.js
+++ b/client/lib/strokes.js
@@ -29,13 +29,15 @@ stages.strokes = class StrokesStage extends stages.AbstractStage {
                 'The final number of paths must agree with the stroke count ' +
                 'in the character metadata.');
     const include = this.include = {};
-    this.strokes = stroke_extractor.getStrokes(glyph).strokes;
+    this.strokes = stroke_extractor.getStrokes(
+        glyph.stages.path, glyph.stages.bridges).strokes;
     this.strokes.map((stroke) => include[stroke] = true);
     if (glyph.stages.strokes && glyph.stages.strokes.length > 0 &&
         glyph.stages.strokes.filter((x) => !include[x]).length === 0) {
       this.strokes.map((stroke) => include[stroke] = false);
       glyph.stages.strokes.map((stroke) => include[stroke] = true);
     }
+    glyph.stages.strokes = this.strokes.filter((x) => this.include[x]);
   }
   handleEvent(glyph, event, template) {
     assert(this.include.hasOwnProperty(template.d));
diff --git a/lib/stroke_extractor.js b/lib/stroke_extractor.js
index 8076b029..6ba67de6 100644
--- a/lib/stroke_extractor.js
+++ b/lib/stroke_extractor.js
@@ -354,9 +354,8 @@ if (this.stroke_extractor !== undefined) {
 }
 this.stroke_extractor = {};
 
-stroke_extractor.getBridges = (glyph, classifier) => {
-  assert(glyph.stages.path)
-  const paths = svg.convertSVGPathToPaths(glyph.stages.path);
+stroke_extractor.getBridges = (path, classifier) => {
+  const paths = svg.convertSVGPathToPaths(path);
   const endpoints = [];
   for (let i = 0; i < paths.length; i++) {
     for (let j = 0; j < paths[i].length; j++) {
@@ -368,10 +367,8 @@ stroke_extractor.getBridges = (glyph, classifier) => {
   return {endpoints: endpoints, bridges: bridges};
 }
 
-stroke_extractor.getStrokes = (glyph) => {
-  assert(glyph.stages.path)
-  assert(glyph.stages.bridges)
-  const paths = svg.convertSVGPathToPaths(glyph.stages.path);
+stroke_extractor.getStrokes = (path, bridges) => {
+  const paths = svg.convertSVGPathToPaths(path);
   const endpoints = [];
   for (let i = 0; i < paths.length; i++) {
     for (let j = 0; j < paths[i].length; j++) {
@@ -379,8 +376,7 @@ stroke_extractor.getStrokes = (glyph) => {
     }
   }
   const log = [];
-  const stroke_paths = extractStrokes(
-      paths, endpoints, glyph.stages.bridges, log);
+  const stroke_paths = extractStrokes(paths, endpoints, bridges, log);
   const strokes = stroke_paths.map((x) => svg.convertPathsToSVGPath([x]));
   return {log: log, strokes: strokes};
 }