diff --git a/tests/Makefile.am b/tests/Makefile.am
index 4116b81a..f576ac12 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -11,6 +11,11 @@ EXTRA_DIST = \
 	tests.h \
 	test_files.sh \
 	test_compress.sh \
+	test_compress_prepared_bcj_sparc \
+	test_compress_prepared_bcj_x86 \
+	test_compress_generated_abc \
+	test_compress_generated_random \
+	test_compress_generated_text \
 	test_scripts.sh \
 	bcj_test.c \
 	compress_prepared_bcj_sparc \
@@ -47,7 +52,11 @@ TESTS = \
 	test_index \
 	test_bcj_exact_size \
 	test_files.sh \
-	test_compress.sh
+	test_compress_prepared_bcj_sparc \
+	test_compress_prepared_bcj_x86 \
+	test_compress_generated_abc \
+	test_compress_generated_random \
+	test_compress_generated_text
 
 if COND_SCRIPTS
 TESTS += test_scripts.sh
diff --git a/tests/test_compress.sh b/tests/test_compress.sh
index 6a486d4c..c88799e7 100755
--- a/tests/test_compress.sh
+++ b/tests/test_compress.sh
@@ -26,7 +26,7 @@ if test $? != 42 ; then
 fi
 
 test_xz() {
-	if $XZ -c "$@" "$FILE" > tmp_compressed; then
+	if $XZ -c "$@" "$FILE" > "$TMP_COMP"; then
 		:
 	else
 		echo "Compressing failed: $* $FILE"
@@ -34,7 +34,7 @@ test_xz() {
 		exit 1
 	fi
 
-	if $XZ -cd tmp_compressed > tmp_uncompressed ; then
+	if $XZ -cd "$TMP_COMP" > "$TMP_UNCOMP" ; then
 		:
 	else
 		echo "Decompressing failed: $* $FILE"
@@ -42,7 +42,7 @@ test_xz() {
 		exit 1
 	fi
 
-	if cmp tmp_uncompressed "$FILE" ; then
+	if cmp "$TMP_UNCOMP" "$FILE" ; then
 		:
 	else
 		echo "Decompressed file does not match" \
@@ -52,7 +52,7 @@ test_xz() {
 	fi
 
 	if test -n "$XZDEC" ; then
-		if $XZDEC tmp_compressed > tmp_uncompressed ; then
+		if $XZDEC "$TMP_COMP" > "$TMP_UNCOMP" ; then
 			:
 		else
 			echo "Decompressing failed: $* $FILE"
@@ -60,7 +60,7 @@ test_xz() {
 			exit 1
 		fi
 
-		if cmp tmp_uncompressed "$FILE" ; then
+		if cmp "$TMP_UNCOMP" "$FILE" ; then
 			:
 		else
 			echo "Decompressed file does not match" \
@@ -76,44 +76,57 @@ XZ="../src/xz/xz --memlimit-compress=48MiB --memlimit-decompress=5MiB \
 XZDEC="../src/xzdec/xzdec" # No memory usage limiter available
 test -x ../src/xzdec/xzdec || XZDEC=
 
-# Create the required input files.
-if ./create_compress_files ; then
-	:
-else
-	rm -f compress_*
-	echo "Failed to create files to test compression."
-	(exit 1)
-	exit 1
-fi
+# Create the required input file if needed.
+FILE=$1
+case $FILE in
+	compress_generated_*)
+		if ./create_compress_files "${FILE#compress_generated_}" ; then
+			:
+		else
+			rm -f "$FILE"
+			echo "Failed to create the file '$FILE'."
+			(exit 1)
+			exit 1
+		fi
+		;;
+	'')
+		echo "No test file was specified."
+		(exit 1)
+		exit 1
+		;;
+esac
+
+# Derive temporary filenames for compressed and uncompressed outputs
+# from the input filename. This is needed when multiple tests are
+# run in parallel.
+TMP_COMP="tmp_comp_${FILE##*/}"
+TMP_UNCOMP="tmp_uncomp_${FILE##*/}"
 
 # Remove temporary now (in case they are something weird), and on exit.
-rm -f tmp_compressed tmp_uncompressed
-trap 'rm -f tmp_compressed tmp_uncompressed' 0
+rm -f "$TMP_COMP" "$TMP_UNCOMP"
+trap 'rm -f "$TMP_COMP" "$TMP_UNCOMP"' 0
 
-# Compress and decompress each file with various filter configurations.
-# This takes quite a bit of time.
-for FILE in compress_generated_* "$srcdir"/compress_prepared_*
+# Compress and decompress the file with various filter configurations.
+#
+# Don't test with empty arguments; it breaks some ancient
+# proprietary /bin/sh versions due to $@ used in test_xz().
+test_xz -1
+test_xz -2
+test_xz -3
+test_xz -4
+
+for ARGS in \
+	--delta=dist=1 \
+	--delta=dist=4 \
+	--delta=dist=256 \
+	--x86 \
+	--powerpc \
+	--ia64 \
+	--arm \
+	--armthumb \
+	--sparc
 do
-	# Don't test with empty arguments; it breaks some ancient
-	# proprietary /bin/sh versions due to $@ used in test_xz().
-	test_xz -1
-	test_xz -2
-	test_xz -3
-	test_xz -4
-
-	for ARGS in \
-		--delta=dist=1 \
-		--delta=dist=4 \
-		--delta=dist=256 \
-		--x86 \
-		--powerpc \
-		--ia64 \
-		--arm \
-		--armthumb \
-		--sparc
-	do
-		test_xz $ARGS --lzma2=dict=64KiB,nice=32,mode=fast
-	done
+	test_xz $ARGS --lzma2=dict=64KiB,nice=32,mode=fast
 done
 
 (exit 0)
diff --git a/tests/test_compress_generated_abc b/tests/test_compress_generated_abc
new file mode 100755
index 00000000..43c69516
--- /dev/null
+++ b/tests/test_compress_generated_abc
@@ -0,0 +1,3 @@
+#!/bin/sh
+
+exec "$srcdir/test_compress.sh" compress_generated_abc
diff --git a/tests/test_compress_generated_random b/tests/test_compress_generated_random
new file mode 100755
index 00000000..e47555d0
--- /dev/null
+++ b/tests/test_compress_generated_random
@@ -0,0 +1,3 @@
+#!/bin/sh
+
+exec "$srcdir/test_compress.sh" compress_generated_random
diff --git a/tests/test_compress_generated_text b/tests/test_compress_generated_text
new file mode 100755
index 00000000..412ae0e9
--- /dev/null
+++ b/tests/test_compress_generated_text
@@ -0,0 +1,3 @@
+#!/bin/sh
+
+exec "$srcdir/test_compress.sh" compress_generated_text
diff --git a/tests/test_compress_prepared_bcj_sparc b/tests/test_compress_prepared_bcj_sparc
new file mode 100755
index 00000000..01447e13
--- /dev/null
+++ b/tests/test_compress_prepared_bcj_sparc
@@ -0,0 +1,3 @@
+#!/bin/sh
+
+exec "$srcdir/test_compress.sh" "$srcdir/compress_prepared_bcj_sparc"
diff --git a/tests/test_compress_prepared_bcj_x86 b/tests/test_compress_prepared_bcj_x86
new file mode 100755
index 00000000..a2771498
--- /dev/null
+++ b/tests/test_compress_prepared_bcj_x86
@@ -0,0 +1,3 @@
+#!/bin/sh
+
+exec "$srcdir/test_compress.sh" "$srcdir/compress_prepared_bcj_x86"