diff --git a/geometry.cpp b/geometry.cpp
index ab41010a..86285deb 100644
--- a/geometry.cpp
+++ b/geometry.cpp
@@ -663,6 +663,7 @@ static std::vector<std::pair<double, double>> clip_poly1(std::vector<std::pair<d
 						// now outside the buffer
 						if (prevent[P_SIMPLIFY_SHARED_NODES]) {
 							out.push_back(intersect(S, E, edge, ax, ay, bx, by));  // on tile boundary
+							edge_nodes.push_back(draw(VT_MOVETO, std::round(out.back().first), std::round(out.back().second)));
 						}
 						out.push_back(intersect(S, E, edge, minx, miny, maxx, maxy));  // on buffer edge
 					} else if (!inside(E, edge, ax, ay, bx, by)) {
@@ -706,6 +707,9 @@ static std::vector<std::pair<double, double>> clip_poly1(std::vector<std::pair<d
 drawvec simple_clip_poly(drawvec &geom, long long minx, long long miny, long long maxx, long long maxy,
 			 long long ax, long long ay, long long bx, long long by, drawvec &edge_nodes) {
 	drawvec out;
+	if (prevent[P_SIMPLIFY_SHARED_NODES]) {
+		geom = remove_noop(geom, VT_POLYGON, 0);
+	}
 
 	for (size_t i = 0; i < geom.size(); i++) {
 		if (geom[i].op == VT_MOVETO) {
@@ -903,9 +907,19 @@ int quick_check(long long *bbox, int z, long long buffer) {
 	long long min = 0;
 	long long area = 1LL << (32 - z);
 
+	// bbox entirely within the tile proper
+	if (bbox[0] > min && bbox[1] > min && bbox[2] < area && bbox[3] < area) {
+		return 1;
+	}
+
 	min -= buffer * area / 256;
 	area += buffer * area / 256;
 
+	// bbox entirely within the tile, including its buffer
+	if (bbox[0] > min && bbox[1] > min && bbox[2] < area && bbox[3] < area) {
+		return 3;
+	}
+
 	// bbox entirely outside the tile
 	if (bbox[0] > area || bbox[1] > area) {
 		return 0;
@@ -914,11 +928,6 @@ int quick_check(long long *bbox, int z, long long buffer) {
 		return 0;
 	}
 
-	// bbox entirely within the tile
-	if (bbox[0] > min && bbox[1] > min && bbox[2] < area && bbox[3] < area) {
-		return 1;
-	}
-
 	// some overlap of edge
 	return 2;
 }
diff --git a/tile.cpp b/tile.cpp
index 566d87ad..3bbca4b1 100644
--- a/tile.cpp
+++ b/tile.cpp
@@ -1408,10 +1408,18 @@ bool clip_to_tile(serial_feature &sf, int z, long long buffer) {
 		}
 	}
 
-	if (quick == 0) {
+	if (quick == 0) {  // entirely outside the tile
 		return true;
 	}
 
+	// if quick == 3 the feature touches the buffer, not just the tile proper,
+	// so we need to clip to add intersection points at the tile edge.
+
+	// if quick == 2 it touches the buffer and beyond, so likewise
+
+	// if quick == 1 we should be able to get away without clipping, because
+	// the feature is entirely within the tile proper.
+
 	// Can't accept the quick check if guaranteeing no duplication, since the
 	// overlap might have been in the buffer.
 	if (quick != 1 || prevent[P_DUPLICATION]) {