diff --git a/geojson/geojson_s2_util.go b/geojson/geojson_s2_util.go
index 5c580643..91ad975e 100644
--- a/geojson/geojson_s2_util.go
+++ b/geojson/geojson_s2_util.go
@@ -25,19 +25,6 @@ import (
 
 // ------------------------------------------------------------------------
 
-// creates a shape index with all of the given polygons
-// and queries it with vertex model closed which considers
-// polygon edges and vertices to be part of the polygon.
-func polygonsContainsPoint(s2pgns []*s2.Polygon,
-	point *s2.Point) bool {
-	idx := s2.NewShapeIndex()
-	for _, s2pgn := range s2pgns {
-		idx.Add(s2pgn)
-	}
-
-	return s2.NewContainsPointQuery(idx, s2.VertexModelClosed).Contains(*point)
-}
-
 // project the point to all of the linestrings and check if
 // any of the projections are equal to the point.
 func polylineIntersectsPoint(pls []*s2.Polyline,
@@ -66,6 +53,21 @@ func polylineIntersectsPolygons(pls []*s2.Polyline,
 	containsQuery := s2.NewContainsPointQuery(idx, s2.VertexModelClosed)
 	for _, pl := range pls {
 		for _, point := range *pl {
+
+			// Precheck points within the bounds of the polygon
+			// and for small polygons, check if the point is contained
+			for _, s2pgn := range s2pgns {
+				if !s2pgn.PointWithinBound(point) {
+					continue
+				}
+
+				if small, inside := s2pgn.SmallPolygonContainsPoint(point); small {
+					if inside {
+						return true
+					}
+				}
+			}
+
 			if containsQuery.Contains(point) {
 				return true
 			}
@@ -95,12 +97,29 @@ func polylineIntersectsPolygons(pls []*s2.Polyline,
 // so we create a shape index and query it instead
 // s2.VertexModelClosed will not consider points on the edges, so
 // behaviour there is arbitrary
-func polygonIntersectsPoint(s2pgns []*s2.Polygon,
+func polygonsIntersectsPoint(s2pgns []*s2.Polygon,
 	point *s2.Point) bool {
 	idx := s2.NewShapeIndex()
 	for _, pgn := range s2pgns {
+		if !pgn.PointWithinBound(*point) {
+			continue
+		}
+
+		// We don't early exit here because the point may be contained
+		// on the vertices of the polygon, which is not considered
+		if small, inside := pgn.SmallPolygonContainsPoint(*point); small {
+			if inside {
+				return true
+			}
+		}
+
 		idx.Add(pgn)
 	}
+
+	if idx.Len() == 0 {
+		return false
+	}
+
 	return s2.NewContainsPointQuery(idx, s2.VertexModelClosed).Contains(*point)
 }
 
diff --git a/geojson/geojson_shapes_impl.go b/geojson/geojson_shapes_impl.go
index 38751abf..7d8e0967 100644
--- a/geojson/geojson_shapes_impl.go
+++ b/geojson/geojson_shapes_impl.go
@@ -933,7 +933,7 @@ func checkPointIntersectsShape(point *s2.Point, shapeIn, other index.GeoJSON) (b
 	// check if the other shape is a polygon.
 	if p2, ok := other.(*Polygon); ok {
 		// check if the point is contained within the polygon.
-		if polygonsContainsPoint([]*s2.Polygon{p2.s2pgn}, point) {
+		if polygonsIntersectsPoint([]*s2.Polygon{p2.s2pgn}, point) {
 			return true, nil
 		}
 
@@ -943,7 +943,7 @@ func checkPointIntersectsShape(point *s2.Point, shapeIn, other index.GeoJSON) (b
 	// check if the other shape is a multipolygon.
 	if p2, ok := other.(*MultiPolygon); ok {
 		// check if the point is contained within any of the polygons
-		if polygonsContainsPoint(p2.s2pgns, point) {
+		if polygonsIntersectsPoint(p2.s2pgns, point) {
 			return true, nil
 		}
 
@@ -1195,7 +1195,7 @@ func checkPolygonIntersectsShape(s2pgn *s2.Polygon, shapeIn,
 	other index.GeoJSON) (bool, error) {
 	// check if the other shape is a point.
 	if p2, ok := other.(*Point); ok {
-		if polygonIntersectsPoint([]*s2.Polygon{s2pgn}, p2.s2point) {
+		if polygonsIntersectsPoint([]*s2.Polygon{s2pgn}, p2.s2point) {
 			return true, nil
 		}
 
@@ -1205,7 +1205,7 @@ func checkPolygonIntersectsShape(s2pgn *s2.Polygon, shapeIn,
 	// check if the other shape is a multipoint.
 	if p2, ok := other.(*MultiPoint); ok {
 		for _, s2point := range p2.s2points {
-			if polygonIntersectsPoint([]*s2.Polygon{s2pgn}, s2point) {
+			if polygonsIntersectsPoint([]*s2.Polygon{s2pgn}, s2point) {
 				return true, nil
 			}
 		}
@@ -1293,10 +1293,8 @@ func checkMultiPolygonContainsShape(s2pgns []*s2.Polygon,
 	shapeIn, other index.GeoJSON) (bool, error) {
 	// check if the other shape is a point.
 	if p2, ok := other.(*Point); ok {
-		for _, s2pgn := range s2pgns {
-			if polygonIntersectsPoint([]*s2.Polygon{s2pgn}, p2.s2point) {
-				return true, nil
-			}
+		if polygonsIntersectsPoint(s2pgns, p2.s2point) {
+			return true, nil
 		}
 
 		return false, nil
diff --git a/s2/polygon.go b/s2/polygon.go
index 7c24805d..94771253 100644
--- a/s2/polygon.go
+++ b/s2/polygon.go
@@ -613,6 +613,27 @@ func (p *Polygon) ContainsPoint(point Point) bool {
 	return NewContainsPointQuery(p.index, VertexModelSemiOpen).Contains(point)
 }
 
+// Check whether the point is within the bounds of the polygon.
+func (p *Polygon) PointWithinBound(point Point) bool {
+	return p.bound.ContainsPoint(point)
+}
+
+// SmallPolygonContainsPoint checks if the polygon is small enough to use brute force
+// returns whether the check is possible and whether the point is contained
+// Does not consider vertices of the polygon
+func (p *Polygon) SmallPolygonContainsPoint(point Point) (bool, bool) {
+	const maxBruteForceVertices = 32
+	if p.numVertices < maxBruteForceVertices || p.index == nil {
+		inside := false
+		for _, l := range p.loops {
+			inside = inside != l.bruteForceContainsPoint(point)
+		}
+		return true, inside
+	}
+
+	return false, false
+}
+
 // ContainsCell reports whether the polygon contains the given cell.
 func (p *Polygon) ContainsCell(cell Cell) bool {
 	it := p.index.Iterator()