diff --git a/.travis.yml b/.travis.yml
index d0f00c5..67228c3 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -6,7 +6,7 @@ compiler:
 
 before_install:
   - sudo apt-get update -qq
-  - sudo apt-get install -qq asciidoc cppcheck libarchive-dev liblzma-dev xz-utils
+  - sudo apt-get install -qq asciidoc cppcheck libarchive-dev liblzma-dev valgrind xz-utils
 
 script:
   - autoconf --version
diff --git a/test/Makefile.am b/test/Makefile.am
index 6aebb6f..808e7b3 100644
--- a/test/Makefile.am
+++ b/test/Makefile.am
@@ -1,6 +1,8 @@
 TESTS = \
 	compress-file-permissions.sh \
 	cppcheck-src.sh \
+	compression-memcheck.sh \
+	decompression-memcheck.sh \
 	single-file-round-trip.sh \
 	xz-compatibility-c-option.sh
 
diff --git a/test/compression-memcheck.sh b/test/compression-memcheck.sh
new file mode 100755
index 0000000..000829b
--- /dev/null
+++ b/test/compression-memcheck.sh
@@ -0,0 +1,22 @@
+#!/bin/bash
+
+if which valgrind &> /dev/null ; then
+  PIXZ=../src/pixz
+
+  INPUT=$(basename $0)
+  OUTPUT=$INPUT.pixz
+
+  MEMCHECK_OUT=$(mktemp)
+
+  trap "rm -f $OUTPUT $MEMCHECK_OUT" EXIT
+
+  valgrind --tool=memcheck --leak-check=full --show-leak-kinds=all --track-origins=yes \
+    $PIXZ $INPUT $OUTPUT \
+      2> $MEMCHECK_OUT
+
+  cat $MEMCHECK_OUT
+  grep -q 'ERROR SUMMARY: 0' $MEMCHECK_OUT
+else
+  echo "no valgrind, skipping test"
+  exit 77
+fi
diff --git a/test/decompression-memcheck.sh b/test/decompression-memcheck.sh
new file mode 100755
index 0000000..c43391a
--- /dev/null
+++ b/test/decompression-memcheck.sh
@@ -0,0 +1,25 @@
+#!/bin/bash
+
+if which valgrind &> /dev/null ; then
+  PIXZ=../src/pixz
+
+  INPUT=$(basename $0)
+  OUTPUT=$INPUT.pixz
+  UNCOMPRESSED=$INPUT.uncompressed
+
+  MEMCHECK_OUT=$(mktemp)
+
+  trap "rm -f $OUTPUT $MEMCHECK_OUT $UNCOMPRESSED" EXIT
+
+  $PIXZ $INPUT $OUTPUT
+
+  valgrind --tool=memcheck --leak-check=full --show-leak-kinds=all --track-origins=yes \
+    $PIXZ -d $OUTPUT $UNCOMPRESSED \
+      2> $MEMCHECK_OUT
+
+  cat $MEMCHECK_OUT
+  grep -q 'ERROR SUMMARY: 0' $MEMCHECK_OUT
+else
+  echo "no valgrind, skipping test"
+  exit 77
+fi