diff --git a/package/pkg-utils.mk b/package/pkg-utils.mk
index 35a441e0aa..d324934dba 100644
--- a/package/pkg-utils.mk
+++ b/package/pkg-utils.mk
@@ -62,8 +62,8 @@ extractor-pkg-dependency = $(EXTRACTOR_PKG_DEPENDENCY$(suffix $(1)))
 # $(firstword) is used here because the extractor can have arguments,
 # like ZCAT="gzip -d -c", and to check for the dependency we only want
 # 'gzip'.
-extractor-system-dependency = $(firstword $(INFLATE$(filter-out \
-	$(EXTRACTOR_DEPENDENCY_PRECHECKED_EXTENSIONS),$(suffix $(1)))))
+extractor-system-dependency = $(if $(EXTRACTOR_PKG_DEPENDENCY$(suffix $(1))),,\
+	$(firstword $(INFLATE$(suffix $(1)))))
 
 # check-deprecated-variable -- throw an error on deprecated variables
 # example:
diff --git a/support/dependencies/check-host-lzip.mk b/support/dependencies/check-host-lzip.mk
index cdd784058c..98a4f42388 100644
--- a/support/dependencies/check-host-lzip.mk
+++ b/support/dependencies/check-host-lzip.mk
@@ -1,5 +1,4 @@
 ifeq (,$(call suitable-host-package,lzip,$(LZCAT)))
 BR2_LZIP_HOST_DEPENDENCY = host-lzip
-EXTRACTOR_DEPENDENCY_PRECHECKED_EXTENSIONS += .lz
 LZCAT = $(HOST_DIR)/bin/lzip -d -c
 endif
diff --git a/support/dependencies/check-host-xzcat.mk b/support/dependencies/check-host-xzcat.mk
index e5d72f95dd..9a78a8f38a 100644
--- a/support/dependencies/check-host-xzcat.mk
+++ b/support/dependencies/check-host-xzcat.mk
@@ -3,6 +3,5 @@
 
 ifeq (,$(call suitable-host-package,xzcat,$(XZCAT)))
 BR2_XZCAT_HOST_DEPENDENCY = host-xz
-EXTRACTOR_DEPENDENCY_PRECHECKED_EXTENSIONS += .xz .lzma
 XZCAT = $(HOST_DIR)/bin/xzcat
 endif