diff --git a/src/main/java/com/conveyal/r5/analyst/WebMercatorGridPointSet.java b/src/main/java/com/conveyal/r5/analyst/WebMercatorGridPointSet.java
index 7c72afd6d..db301b28d 100644
--- a/src/main/java/com/conveyal/r5/analyst/WebMercatorGridPointSet.java
+++ b/src/main/java/com/conveyal/r5/analyst/WebMercatorGridPointSet.java
@@ -1,10 +1,14 @@
 package com.conveyal.r5.analyst;
 
+import com.conveyal.r5.common.SphericalDistanceLibrary;
 import com.conveyal.r5.profile.StreetMode;
 import com.conveyal.r5.streets.LinkedPointSet;
+import com.conveyal.r5.streets.Split;
 import com.conveyal.r5.streets.StreetLayer;
+import com.conveyal.r5.transit.TransitLayer;
 import com.conveyal.r5.transit.TransportNetwork;
 import com.vividsolutions.jts.geom.Coordinate;
+import com.vividsolutions.jts.geom.Envelope;
 import org.mapdb.Fun;
 import org.slf4j.Logger;
 import org.slf4j.LoggerFactory;
@@ -50,10 +54,15 @@ public WebMercatorGridPointSet(TransportNetwork transportNetwork) {
         LOG.info("Creating web mercator pointset for transport network with extents {}", transportNetwork.streetLayer.envelope);
 
         this.zoom = DEFAULT_ZOOM;
-        int west = lonToPixel(transportNetwork.streetLayer.envelope.getMinX());
-        int east = lonToPixel(transportNetwork.streetLayer.envelope.getMaxX());
-        int north = latToPixel(transportNetwork.streetLayer.envelope.getMaxY());
-        int south = latToPixel(transportNetwork.streetLayer.envelope.getMinY());
+
+        double latBuffer = SphericalDistanceLibrary.metersToDegreesLatitude(LinkedPointSet.MAX_OFFSTREET_WALK_METERS);
+        double lonBuffer = SphericalDistanceLibrary
+                .metersToDegreesLongitude(LinkedPointSet.MAX_OFFSTREET_WALK_METERS, transportNetwork.streetLayer.envelope.centre().y);
+
+        int west = lonToPixel(transportNetwork.streetLayer.envelope.getMinX() - lonBuffer);
+        int east = lonToPixel(transportNetwork.streetLayer.envelope.getMaxX() + lonBuffer);
+        int north = latToPixel(transportNetwork.streetLayer.envelope.getMaxY() + latBuffer);
+        int south = latToPixel(transportNetwork.streetLayer.envelope.getMinY() - latBuffer);
 
         this.west = west;
         this.north = north;
diff --git a/src/main/java/com/conveyal/r5/streets/LinkedPointSet.java b/src/main/java/com/conveyal/r5/streets/LinkedPointSet.java
index 8c8630e04..93cea8444 100644
--- a/src/main/java/com/conveyal/r5/streets/LinkedPointSet.java
+++ b/src/main/java/com/conveyal/r5/streets/LinkedPointSet.java
@@ -161,7 +161,9 @@ public LinkedPointSet(LinkedPointSet sourceLinkage, WebMercatorGridPointSet subG
         }
         if (superGrid.west > subGrid.west || superGrid.west + superGrid.width < subGrid.west + subGrid.width ||
             superGrid.north > subGrid.north || superGrid.north + superGrid.height < subGrid.north + subGrid.height) {
-            throw new IllegalArgumentException("Sub-grid must lie fully inside the super-grid.");
+            // we simply warn if it does not lie within the super grid. This used to throw an error but that prevents
+            // analyses with origins near the edge of the graph.
+            LOG.warn("Part of sub-grid does not lie with super grid");
         }
 
         // Initialize the fields of the new LinkedPointSet instance
@@ -174,10 +176,22 @@ public LinkedPointSet(LinkedPointSet sourceLinkage, WebMercatorGridPointSet subG
         distances0_mm = new int[nCells];
         distances1_mm = new int[nCells];
 
+        // mark all points as unlinked, in case part of the subGrid lies outside the super grid. Points within the super
+        // grid will be overwritten below
+        Arrays.fill(edges, -1);
+
         // Copy values over from the source linkage to the new sub-linkage
         // x, y, and pixel are relative to the new linkage
         for (int y = 0, pixel = 0; y < subGrid.height; y++) {
+            int row = subGrid.north + y;
+            boolean rowWithinSuperGrid = row >= superGrid.north && row < superGrid.north + superGrid.height;
+            if (!rowWithinSuperGrid) continue;
+
             for (int x = 0; x < subGrid.width; x++, pixel++) {
+                int col = subGrid.west + x;
+                boolean colWithinSuperGrid = col >= superGrid.west && col < superGrid.west + superGrid.width;
+                if (!colWithinSuperGrid) continue;
+
                 int sourceColumn = subGrid.west + x - superGrid.west;
                 int sourceRow = subGrid.north + y - superGrid.north;
                 int sourcePixel = sourceRow * superGrid.width + sourceColumn;