diff --git a/meta/lib/oeqa/selftest/sstatetests.py b/meta/lib/oeqa/selftest/sstatetests.py
index c4efc47..3c23062 100644
--- a/meta/lib/oeqa/selftest/sstatetests.py
+++ b/meta/lib/oeqa/selftest/sstatetests.py
@@ -34,7 +34,7 @@
         targetarch = get_bb_var('TUNE_ARCH')
         self.run_test_sstate_creation(['binutils-cross-'+ targetarch, 'binutils-native'], distro_specific=True, distro_nonspecific=False, temp_sstate_location=True)
 
-    @testcase(975)
+    @testcase(1374)
     def test_sstate_creation_distro_specific_fail(self):
         targetarch = get_bb_var('TUNE_ARCH')
         self.run_test_sstate_creation(['binutils-cross-'+ targetarch, 'binutils-native'], distro_specific=False, distro_nonspecific=True, temp_sstate_location=True, should_pass=False)
@@ -43,7 +43,7 @@
     def test_sstate_creation_distro_nonspecific_pass(self):
         self.run_test_sstate_creation(['glibc-initial'], distro_specific=False, distro_nonspecific=True, temp_sstate_location=True)
 
-    @testcase(976)
+    @testcase(1375)
     def test_sstate_creation_distro_nonspecific_fail(self):
         self.run_test_sstate_creation(['glibc-initial'], distro_specific=True, distro_nonspecific=False, temp_sstate_location=True, should_pass=False)
 
@@ -70,11 +70,11 @@
         targetarch = get_bb_var('TUNE_ARCH')
         self.run_test_cleansstate_task(['binutils-cross-' + targetarch, 'binutils-native', 'glibc-initial'], distro_specific=True, distro_nonspecific=True, temp_sstate_location=True)
 
-    @testcase(977)
+    @testcase(1376)
     def test_cleansstate_task_distro_nonspecific(self):
         self.run_test_cleansstate_task(['glibc-initial'], distro_specific=False, distro_nonspecific=True, temp_sstate_location=True)
 
-    @testcase(977)
+    @testcase(1377)
     def test_cleansstate_task_distro_specific(self):
         targetarch = get_bb_var('TUNE_ARCH')
         self.run_test_cleansstate_task(['binutils-cross-'+ targetarch, 'binutils-native', 'glibc-initial'], distro_specific=True, distro_nonspecific=False, temp_sstate_location=True)
@@ -111,12 +111,12 @@
         targetarch = get_bb_var('TUNE_ARCH')
         self.run_test_rebuild_distro_specific_sstate(['binutils-cross-' + targetarch, 'binutils-native'], temp_sstate_location=True)
 
-    @testcase(175)
+    @testcase(1372)
     def test_rebuild_distro_specific_sstate_cross_target(self):
         targetarch = get_bb_var('TUNE_ARCH')
         self.run_test_rebuild_distro_specific_sstate(['binutils-cross-' + targetarch], temp_sstate_location=True)
 
-    @testcase(175)
+    @testcase(1373)
     def test_rebuild_distro_specific_sstate_native_target(self):
         self.run_test_rebuild_distro_specific_sstate(['binutils-native'], temp_sstate_location=True)
 
@@ -211,6 +211,8 @@
         they're built on a 32 or 64 bit system. Rather than requiring two different 
         build machines and running a builds, override the variables calling uname()
         manually and check using bitbake -S.
+        
+        Also check that SDKMACHINE changing doesn't change any of these stamps.
         """
 
         topdir = get_bb_var('TOPDIR')
@@ -219,6 +221,7 @@
 TMPDIR = \"${TOPDIR}/tmp-sstatesamehash\"
 BUILD_ARCH = \"x86_64\"
 BUILD_OS = \"linux\"
+SDKMACHINE = \"x86_64\"
 """)
         self.track_for_cleanup(topdir + "/tmp-sstatesamehash")
         bitbake("core-image-sato -S none")
@@ -226,6 +229,7 @@
 TMPDIR = \"${TOPDIR}/tmp-sstatesamehash2\"
 BUILD_ARCH = \"i686\"
 BUILD_OS = \"linux\"
+SDKMACHINE = \"i686\"
 """)
         self.track_for_cleanup(topdir + "/tmp-sstatesamehash2")
         bitbake("core-image-sato -S none")
@@ -233,11 +237,16 @@
         def get_files(d):
             f = []
             for root, dirs, files in os.walk(d):
+                if "core-image-sato" in root:
+                        # SDKMACHINE changing will change do_rootfs/do_testimage/do_build stamps of core-image-sato itself
+                        # which is safe to ignore
+                        continue
                 f.extend(os.path.join(root, name) for name in files)
             return f
         files1 = get_files(topdir + "/tmp-sstatesamehash/stamps/")
         files2 = get_files(topdir + "/tmp-sstatesamehash2/stamps/")
         files2 = [x.replace("tmp-sstatesamehash2", "tmp-sstatesamehash").replace("i686-linux", "x86_64-linux").replace("i686" + targetvendor + "-linux", "x86_64" + targetvendor + "-linux", ) for x in files2]
+        self.maxDiff = None
         self.assertItemsEqual(files1, files2)
 
 
@@ -271,11 +280,13 @@
         files1 = get_files(topdir + "/tmp-sstatesamehash/stamps/")
         files2 = get_files(topdir + "/tmp-sstatesamehash2/stamps/")
         files2 = [x.replace("tmp-sstatesamehash2", "tmp-sstatesamehash") for x in files2]
+        self.maxDiff = None
         self.assertItemsEqual(files1, files2)
 
+    @testcase(1368)
     def test_sstate_allarch_samesigs(self):
         """
-        The sstate checksums off allarch packages should be independent of whichever 
+        The sstate checksums of allarch packages should be independent of whichever 
         MACHINE is set. Check this using bitbake -S.
         Also, rather than duplicate the test, check nativesdk stamps are the same between
         the two MACHINE values.
@@ -319,4 +330,50 @@
         files2 = [x.replace("tmp-sstatesamehash2", "tmp-sstatesamehash") for x in files2]
         self.maxDiff = None
         self.assertItemsEqual(files1, files2)
-        
+
+    @testcase(1369)
+    def test_sstate_sametune_samesigs(self):
+        """
+        The sstate checksums of two identical machines (using the same tune) should be the 
+        same, apart from changes within the machine specific stamps directory. We use the
+        qemux86copy machine to test this. Also include multilibs in the test.
+        """
+
+        topdir = get_bb_var('TOPDIR')
+        targetos = get_bb_var('TARGET_OS')
+        targetvendor = get_bb_var('TARGET_VENDOR')
+        self.write_config("""
+TMPDIR = \"${TOPDIR}/tmp-sstatesamehash\"
+MACHINE = \"qemux86\"
+require conf/multilib.conf
+MULTILIBS = "multilib:lib32"
+DEFAULTTUNE_virtclass-multilib-lib32 = "x86"
+""")
+        self.track_for_cleanup(topdir + "/tmp-sstatesamehash")
+        bitbake("world meta-toolchain -S none")
+        self.write_config("""
+TMPDIR = \"${TOPDIR}/tmp-sstatesamehash2\"
+MACHINE = \"qemux86copy\"
+require conf/multilib.conf
+MULTILIBS = "multilib:lib32"
+DEFAULTTUNE_virtclass-multilib-lib32 = "x86"
+""")
+        self.track_for_cleanup(topdir + "/tmp-sstatesamehash2")
+        bitbake("world meta-toolchain -S none")
+
+        def get_files(d):
+            f = []
+            for root, dirs, files in os.walk(d):
+                for name in files:
+                    if "meta-environment" in root or "cross-canadian" in root:
+                        continue
+                    if "qemux86copy-" in root or "qemux86-" in root:
+                        continue
+                    if "do_build" not in name and "do_populate_sdk" not in name:
+                        f.append(os.path.join(root, name))
+            return f
+        files1 = get_files(topdir + "/tmp-sstatesamehash/stamps")
+        files2 = get_files(topdir + "/tmp-sstatesamehash2/stamps")
+        files2 = [x.replace("tmp-sstatesamehash2", "tmp-sstatesamehash") for x in files2]
+        self.maxDiff = None
+        self.assertItemsEqual(files1, files2)