diff --git a/src/main/java/com/conveyal/r5/analyst/FreeFormPointSet.java b/src/main/java/com/conveyal/r5/analyst/FreeFormPointSet.java
index 4e9527be5..d0deaed13 100644
--- a/src/main/java/com/conveyal/r5/analyst/FreeFormPointSet.java
+++ b/src/main/java/com/conveyal/r5/analyst/FreeFormPointSet.java
@@ -251,8 +251,7 @@ public Envelope getWgsEnvelope () {
     public WebMercatorExtents getWebMercatorExtents () {
         final int DEFAULT_ZOOM = 9;
         Envelope wgsEnvelope = this.getWgsEnvelope();
-        WebMercatorExtents webMercatorExtents = WebMercatorExtents.forWgsEnvelope(wgsEnvelope, DEFAULT_ZOOM);
-        return webMercatorExtents;
+        return WebMercatorExtents.forBufferedWgsEnvelope(wgsEnvelope, DEFAULT_ZOOM);
     }
 
     /** Construct a freeform point set containing one opportunity at each specified geographic coordinate. */
diff --git a/src/main/java/com/conveyal/r5/analyst/Grid.java b/src/main/java/com/conveyal/r5/analyst/Grid.java
index a47021b0f..d3d113ff1 100644
--- a/src/main/java/com/conveyal/r5/analyst/Grid.java
+++ b/src/main/java/com/conveyal/r5/analyst/Grid.java
@@ -123,7 +123,7 @@ public Grid (WebMercatorExtents extents) {
      * @param wgsEnvelope Envelope of grid, in absolute WGS84 lat/lon coordinates
      */
     public Grid (int zoom, Envelope wgsEnvelope) {
-        this(WebMercatorExtents.forWgsEnvelope(wgsEnvelope, zoom));
+        this(WebMercatorExtents.forBufferedWgsEnvelope(wgsEnvelope, zoom));
     }
 
     public static class PixelWeight {
@@ -618,7 +618,7 @@ public static List<Grid> fromCsv(InputStreamProvider csvInputStreamProvider,
         reader.close();
 
         checkWgsEnvelopeSize(envelope, "CSV points");
-        WebMercatorExtents extents = WebMercatorExtents.forWgsEnvelope(envelope, zoom);
+        WebMercatorExtents extents = WebMercatorExtents.forBufferedWgsEnvelope(envelope, zoom);
         checkPixelCount(extents, numericColumns.size());
 
         if (progressListener != null) {
@@ -690,7 +690,7 @@ public static List<Grid> fromShapefile (File shapefile, int zoom, ProgressListen
         ShapefileReader reader = new ShapefileReader(shapefile);
         Envelope envelope = reader.wgs84Bounds();
         checkWgsEnvelopeSize(envelope, "Shapefile");
-        WebMercatorExtents extents = WebMercatorExtents.forWgsEnvelope(envelope, zoom);
+        WebMercatorExtents extents = WebMercatorExtents.forBufferedWgsEnvelope(envelope, zoom);
         List<String> numericAttributes = reader.numericAttributes();
         Set<String> uniqueNumericAttributes = new HashSet<>(numericAttributes);
         if (uniqueNumericAttributes.size() != numericAttributes.size()) {
@@ -772,7 +772,7 @@ public double getOpportunityCount (int i) {
     public static Grid fromFreeForm (FreeFormPointSet freeForm, int zoom) {
         // TODO make and us a strongly typed WgsEnvelope class here and in various places
         Envelope wgsEnvelope = freeForm.getWgsEnvelope();
-        WebMercatorExtents webMercatorExtents = WebMercatorExtents.forWgsEnvelope(wgsEnvelope, zoom);
+        WebMercatorExtents webMercatorExtents = WebMercatorExtents.forBufferedWgsEnvelope(wgsEnvelope, zoom);
         Grid grid = new Grid(webMercatorExtents);
         grid.name = freeForm.name;
         for (int f = 0; f < freeForm.featureCount(); f++) {
diff --git a/src/main/java/com/conveyal/r5/analyst/WebMercatorExtents.java b/src/main/java/com/conveyal/r5/analyst/WebMercatorExtents.java
index cff116c00..d332d32f6 100644
--- a/src/main/java/com/conveyal/r5/analyst/WebMercatorExtents.java
+++ b/src/main/java/com/conveyal/r5/analyst/WebMercatorExtents.java
@@ -184,6 +184,18 @@ public static WebMercatorExtents forTrimmedWgsEnvelope (Envelope wgsEnvelope, in
         return WebMercatorExtents.forWgsEnvelope(wgsEnvelope, zoom);
     }
 
+    /**
+     * The opposite of forTrimmedWgsEnvelope: makes the envelope a tiny bit bigger before constructing the extents.
+     * This helps deal with numerical imprecision where we want to be sure all points within a supplied envelope will
+     * fall inside cells of the resulting web Mercator grid.
+     */
+    public static WebMercatorExtents forBufferedWgsEnvelope (Envelope wgsEnvelope, int zoom) {
+        // Expand a protective copy of the envelope slightly.
+        wgsEnvelope = wgsEnvelope.copy();
+        wgsEnvelope.expandBy(WGS_EPSILON);
+        return WebMercatorExtents.forWgsEnvelope(wgsEnvelope, zoom);
+    }
+
     /**
      * Produces a new Envelope in WGS84 coordinates that tightly encloses the pixels of this WebMercatorExtents.
      * The edges of that Envelope will run exactly down the borders between neighboring web Mercator pixels.