diff --git a/crypto_kem/kyber768/clean/GNUmakefile b/crypto_kem/kyber768/clean/GNUmakefile
deleted file mode 100644
index b7ad903a..00000000
--- a/crypto_kem/kyber768/clean/GNUmakefile
+++ /dev/null
@@ -1,15 +0,0 @@
-LIB=libkyber768_clean.a
-
-SOURCES=$(wildcard *.c)
-OBJECTS=$(patsubst %.c,%.o,$(SOURCES))
-
-CFLAGS=-Wall -Wextra -Wpedantic -Werror -std=c99 -I../../../common $(EXTRAFLAGS)
-
-all: $(LIB)
-
-$(LIB): $(OBJECTS)
-	$(AR) -r $@ $(OBJECTS)
-
-clean:
-	$(RM) $(OBJECTS)
-	$(RM) $(LIB)
diff --git a/crypto_kem/kyber768/clean/Makefile b/crypto_kem/kyber768/clean/Makefile
index 616dcbf3..30340cc6 100644
--- a/crypto_kem/kyber768/clean/Makefile
+++ b/crypto_kem/kyber768/clean/Makefile
@@ -1,4 +1,4 @@
-# This Makefile has been tested with GNU Make and BSD Make
+# This Makefile can be used with GNU Make or BSD Make
 
 LIB=libkyber768_clean.a
 OBJECTS=cbd.o indcpa.o kem.o kex.o ntt.o poly.o polyvec.o precomp.o reduce.o verify.o
diff --git a/crypto_sign/dilithium-iii/clean/Makefile b/crypto_sign/dilithium-iii/clean/Makefile
new file mode 100644
index 00000000..39e83ed7
--- /dev/null
+++ b/crypto_sign/dilithium-iii/clean/Makefile
@@ -0,0 +1,15 @@
+# This Makefile can be used with GNU Make or BSD Make
+
+LIB=libdilithium-iii_clean.a
+OBJECTS=ntt.o packing.o poly.o polyvec.o reduce.o rounding.o sign.o
+
+CFLAGS=-Wall -Wextra -Wpedantic -Werror -std=c99 -I../../../common $(EXTRAFLAGS)
+
+all: $(LIB)
+
+$(LIB): $(OBJECTS)
+    $(AR) -r $@ $(OBJECTS)
+
+clean:
+    $(RM) $(OBJECTS)
+    $(RM) $(LIB)
diff --git a/crypto_sign/dilithium-iii/clean/Makefile.Microsoft_nmake b/crypto_sign/dilithium-iii/clean/Makefile.Microsoft_nmake
index 6b79e019..18cc6db9 100644
--- a/crypto_sign/dilithium-iii/clean/Makefile.Microsoft_nmake
+++ b/crypto_sign/dilithium-iii/clean/Makefile.Microsoft_nmake
@@ -1,8 +1,10 @@
-LIB=libdilithium-iii_clean.lib
+# This Makefile can be used with Microsoft Visual Studio's nmake using the command:
+#    nmake /f Makefile.Microsoft_nmake
 
+LIB=libdilithium-iii_clean.lib
 OBJECTS=ntt.obj packing.obj poly.obj polyvec.obj reduce.obj rounding.obj sign.obj
 
-CFLAGS=/I ..\..\..\common /W1 /WX
+CFLAGS=/I ..\..\..\common /W1 /WX # FIXME: ideally would use /W4 instead of /W1, but too many failures in Dilithium right now
 
 all: $(LIB)