diff --git a/geojson.c b/geojson.c
index cc9d499..2d347e8 100644
--- a/geojson.c
+++ b/geojson.c
@@ -160,7 +160,7 @@ void parse_geometry(int t, json_object *j, unsigned *bbox, long long *fpos, FILE
 		}
 	} else {
 		if (j->length >= 2 && j->array[0]->type == JSON_NUMBER && j->array[1]->type == JSON_NUMBER) {
-			unsigned x, y;
+			long long x, y;
 			double lon = j->array[0]->number;
 			double lat = j->array[1]->number;
 			latlon2tile(lat, lon, 32, &x, &y);
diff --git a/projection.c b/projection.c
index effb347..839370e 100644
--- a/projection.c
+++ b/projection.c
@@ -2,39 +2,19 @@
 #include "projection.h"
 
 // http://wiki.openstreetmap.org/wiki/Slippy_map_tilenames
-void latlon2tile(double lat, double lon, int zoom, unsigned int *x, unsigned int *y) {
+void latlon2tile(double lat, double lon, int zoom, long long *x, long long *y) {
 	double lat_rad = lat * M_PI / 180;
 	unsigned long long n = 1LL << zoom;
 
 	long long llx = n * ((lon + 180) / 360);
 	long long lly = n * (1 - (log(tan(lat_rad) + 1 / cos(lat_rad)) / M_PI)) / 2;
 
-	if (lat >= 85.0511) {
-		lly = 0;
-	}
-	if (lat <= -85.0511) {
-		lly = n - 1;
-	}
-
-	if (llx < 0) {
-		llx = 0;
-	}
-	if (lly < 0) {
-		lly = 0;
-	}
-	if (llx >= n) {
-		llx = n - 1;
-	}
-	if (lly >= n) {
-		lly = n - 1;
-	}
-
 	*x = llx;
 	*y = lly;
 }
 
 // http://wiki.openstreetmap.org/wiki/Slippy_map_tilenames
-void tile2latlon(unsigned int x, unsigned int y, int zoom, double *lat, double *lon) {
+void tile2latlon(long long x, long long y, int zoom, double *lat, double *lon) {
 	unsigned long long n = 1LL << zoom;
 	*lon = 360.0 * x / n - 180.0;
 	*lat = atan(sinh(M_PI * (1 - 2.0 * y / n))) * 180.0 / M_PI;
diff --git a/projection.h b/projection.h
index af7002e..20d67ec 100644
--- a/projection.h
+++ b/projection.h
@@ -1,4 +1,4 @@
-void latlon2tile(double lat, double lon, int zoom, unsigned int *x, unsigned int *y);
-void tile2latlon(unsigned int x, unsigned int y, int zoom, double *lat, double *lon);
+void latlon2tile(double lat, double lon, int zoom, long long *x, long long *y);
+void tile2latlon(long long x, long long y, int zoom, double *lat, double *lon);
 unsigned long long encode(unsigned int wx, unsigned int wy);
 void decode(unsigned long long index, unsigned *wx, unsigned *wy);
diff --git a/tile.cc b/tile.cc
index bdd95a6..6daa00a 100644
--- a/tile.cc
+++ b/tile.cc
@@ -544,6 +544,26 @@ long long write_tile(char **geoms, char *metabase, char *stringpool, int z, unsi
 				continue;
 			}
 
+			if (z == 0) {
+				if (bbox[0] < 0 || bbox[2] > 1LL << 32) {
+					// If the geometry extends off the edge of the world, concatenate on another copy
+					// shifted by 360 degrees, and then make sure both copies get clipped down to size.
+
+					unsigned n = geom.size();
+					for (unsigned i = 0; i < n; i++) {
+						geom.push_back(draw(geom[i].op, geom[i].x - (1LL << 32), geom[i].y));
+					}
+					for (unsigned i = 0; i < n; i++) {
+						geom.push_back(draw(geom[i].op, geom[i].x + (1LL << 32), geom[i].y));
+					}
+
+					bbox[0] = 0;
+					bbox[2] = 1LL << 32;
+
+					quick = -1;
+				}
+			}
+
 			if (quick != 1) {
 				if (t == VT_LINE) {
 					geom = clip_lines(geom, z, line_detail, buffer);