diff --git a/Makefile b/Makefile
index becde1f18..33657b25c 100644
--- a/Makefile
+++ b/Makefile
@@ -18,12 +18,12 @@ font: $(EMOJI).ttf
 
 CFLAGS = -std=c99 -Wall -Wextra `pkg-config --cflags --libs cairo`
 LDFLAGS = `pkg-config --libs cairo`
-PNGQUANTDIR := $(abspath `pwd`/../third_party/pngquant)
+PNGQUANTDIR := third_party/pngquant
 PNGQUANT := $(PNGQUANTDIR)/pngquant
 PNGQUANTFLAGS = --speed 1 --skip-if-larger --ext '.png' --force
 
-"$(PNGQUANT)":
-	cd "$(PNGQUANTDIR)" && make
+$(PNGQUANT):
+	$(MAKE) -C $(PNGQUANTDIR)
 
 waveflag: waveflag.c
 	$(CC) $< -o $@ $(CFLAGS) $(LDFLAGS)
@@ -62,11 +62,11 @@ GLYPH_NAMES := $(shell ./flag_glyph_name.py $(FLAGS))
 WAVED_FLAGS := $(foreach flag,$(FLAGS),$(FLAGS_DIR)/$(flag).png)
 PNG128_FLAGS := $(foreach glyph_name,$(GLYPH_NAMES),$(addprefix ./png/128/emoji_$(glyph_name),.png))
 
-$(FLAGS_DIR)/%.png: $(FLAGS_SRC_DIR)/%.png ./waveflag "$(PNGQUANT)"
+$(FLAGS_DIR)/%.png: $(FLAGS_SRC_DIR)/%.png ./waveflag $(PNGQUANT)
 	mkdir -p $(FLAGS_DIR)
 	./waveflag "$<" "$@"
 	optipng -quiet -o7 "$@"
-	"$(PNGQUANT)" $(PNGQUANTFLAGS) "$@"
+	$(PNGQUANT) $(PNGQUANTFLAGS) "$@"
 
 flag-symlinks: $(WAVED_FLAGS)
 	$(subst ^, ,                                \
@@ -85,7 +85,7 @@ ADD_GLYPHS = third_party/color_emoji/add_glyphs.py
 PUA_ADDER = map_pua_emoji.py
 VS_ADDER = add_vs_cmap.py
 
-%.ttx: %.ttx.tmpl $(ADD_GLYPHS) $(UNI) flag-symlinks
+%.ttx: %.ttx.tmpl $(ADD_GLYPHS) $(UNI) $(PNG128_FLAGS)
 	python $(ADD_GLYPHS) "$<" "$@" "$(EMOJI_PNG128)"
 
 %.ttf: %.ttx
@@ -93,7 +93,7 @@ VS_ADDER = add_vs_cmap.py
 	ttx "$<"
 
 $(EMOJI).ttf: $(EMOJI).tmpl.ttf $(EMOJI_BUILDER) $(PUA_ADDER) $(VS_ADDER) \
-  $(EMOJI_PNG128)*.png flag-symlinks
+  $(EMOJI_PNG128)*.png $(PNG128_FLAGS)
 	python $(EMOJI_BUILDER) -V $< "$@" $(EMOJI_PNG128)
 	python $(PUA_ADDER) "$@" "$@-with-pua"
 	$(VS_ADDER) --dstdir '.' -o "$@-with-pua-varsel" "$@-with-pua"