diff --git a/filling.c b/filling.c
index f47f9f1..b05ab49 100644
--- a/filling.c
+++ b/filling.c
@@ -907,7 +907,7 @@ static void game_changed_state(game_ui *ui, game_state *oldstate,
 #define PREFERRED_TILE_SIZE 32
 #define TILE_SIZE (ds->tilesize)
 #define BORDER (TILE_SIZE / 2)
-#define BORDER_WIDTH (TILE_SIZE / 32)
+#define BORDER_WIDTH (max(TILE_SIZE / 32, 1))
 
 struct game_drawstate {
     struct game_params params;
diff --git a/galaxies.c b/galaxies.c
index 6989fe3..bfb558d 100644
--- a/galaxies.c
+++ b/galaxies.c
@@ -2075,7 +2075,7 @@ static void game_changed_state(game_ui *ui, game_state *oldstate,
 #define PREFERRED_TILE_SIZE 32
 #define TILE_SIZE (ds->tilesize)
 #define DOT_SIZE        (TILE_SIZE / 4)
-#define EDGE_THICKNESS (TILE_SIZE / 16)
+#define EDGE_THICKNESS (max(TILE_SIZE / 16, 2))
 #define BORDER TILE_SIZE
 
 #define COORD(x) ( (x) * TILE_SIZE + BORDER )