diff --git a/easybuild/tools/systemtools.py b/easybuild/tools/systemtools.py
index d58cfc0abf..6a3aa83861 100644
--- a/easybuild/tools/systemtools.py
+++ b/easybuild/tools/systemtools.py
@@ -73,6 +73,8 @@
 POWER = 'POWER'
 X86_64 = 'x86_64'
 
+ARCH_KEY_PREFIX = 'arch='
+
 # Vendor constants
 AMD = 'AMD'
 APM = 'Applied Micro'
@@ -921,20 +923,29 @@ def pick_dep_version(dep_version):
         result = None
 
     elif isinstance(dep_version, dict):
-        # figure out matches based on dict keys (after splitting on '=')
-        my_arch_key = 'arch=%s' % get_cpu_architecture()
-        arch_keys = [x for x in dep_version.keys() if x.startswith('arch=')]
+        arch_keys = [x for x in dep_version.keys() if x.startswith(ARCH_KEY_PREFIX)]
         other_keys = [x for x in dep_version.keys() if x not in arch_keys]
         if other_keys:
-            raise EasyBuildError("Unexpected keys in version: %s. Only 'arch=' keys are supported", other_keys)
+            other_keys = ','.join(sorted(other_keys))
+            raise EasyBuildError("Unexpected keys in version: %s (only 'arch=' keys are supported)", other_keys)
         if arch_keys:
-            if my_arch_key in dep_version:
-                result = dep_version[my_arch_key]
-                _log.info("Version selected from %s using key %s: %s", dep_version, my_arch_key, result)
+            host_arch_key = ARCH_KEY_PREFIX + get_cpu_architecture()
+            star_arch_key = ARCH_KEY_PREFIX + '*'
+            # check for specific 'arch=' key first
+            if host_arch_key in dep_version:
+                result = dep_version[host_arch_key]
+                _log.info("Version selected from %s using key %s: %s", dep_version, host_arch_key, result)
+            # fall back to 'arch=*'
+            elif star_arch_key in dep_version:
+                result = dep_version[star_arch_key]
+                _log.info("Version selected for %s using fallback key %s: %s", dep_version, star_arch_key, result)
             else:
-                raise EasyBuildError("No matches for version in %s (looking for %s)", dep_version, my_arch_key)
+                raise EasyBuildError("No matches for version in %s (looking for %s)", dep_version, host_arch_key)
+        else:
+            raise EasyBuildError("Found empty dict as version!")
 
     else:
-        raise EasyBuildError("Unknown value type for version: %s", dep_version)
+        typ = type(dep_version)
+        raise EasyBuildError("Unknown value type for version: %s (%s), should be string value", typ, dep_version)
 
     return result
diff --git a/test/framework/easyconfig.py b/test/framework/easyconfig.py
index d4011f124f..d5d6458ef0 100644
--- a/test/framework/easyconfig.py
+++ b/test/framework/easyconfig.py
@@ -72,7 +72,7 @@
 from easybuild.tools.options import parse_external_modules_metadata
 from easybuild.tools.py2vs3 import OrderedDict, reload
 from easybuild.tools.robot import resolve_dependencies
-from easybuild.tools.systemtools import get_shared_lib_ext
+from easybuild.tools.systemtools import AARCH64, POWER, X86_64, get_cpu_architecture, get_shared_lib_ext
 from easybuild.tools.toolchain.utilities import search_toolchain
 from easybuild.tools.utilities import quote_str, quote_py_str
 from test.framework.utilities import find_full_path
@@ -104,6 +104,7 @@ class EasyConfigTest(EnhancedTestCase):
     def setUp(self):
         """Set up everything for running a unit test."""
         super(EasyConfigTest, self).setUp()
+        self.orig_get_cpu_architecture = st.get_cpu_architecture
 
         self.cwd = os.getcwd()
         self.all_stops = [x[0] for x in EasyBlock.get_steps()]
@@ -122,6 +123,7 @@ def prep(self):
 
     def tearDown(self):
         """ make sure to remove the temporary file """
+        st.get_cpu_architecture = self.orig_get_cpu_architecture
         super(EasyConfigTest, self).tearDown()
         if os.path.exists(self.eb_file):
             os.remove(self.eb_file)
@@ -305,6 +307,69 @@ def test_dependency(self):
         self.assertErrorRegex(EasyBuildError, err_msg, eb._parse_dependency, (EXTERNAL_MODULE_MARKER,))
         self.assertErrorRegex(EasyBuildError, err_msg, eb._parse_dependency, ('foo', '1.2.3', EXTERNAL_MODULE_MARKER))
 
+    def test_false_dep_version(self):
+        """
+        Test use False as dependency version via dict using 'arch=' keys,
+        which should result in filtering the dependency.
+        """
+        # silence warnings about missing easyconfigs for dependencies, we don't care
+        init_config(build_options={'silent': True})
+
+        arch = get_cpu_architecture()
+
+        self.contents = '\n'.join([
+            'easyblock = "ConfigureMake"',
+            'name = "pi"',
+            'version = "3.14"',
+            'versionsuffix = "-test"',
+            'homepage = "http://example.com"',
+            'description = "test easyconfig"',
+            'toolchain = {"name":"GCC", "version": "4.6.3"}',
+            'builddependencies = [',
+            '   ("first_build", {"arch=%s": False}),' % arch,
+            '   ("second_build", "2.0"),',
+            ']',
+            'dependencies = ['
+            '   ("first", "1.0"),',
+            '   ("second", {"arch=%s": False}),' % arch,
+            ']',
+        ])
+        self.prep()
+        eb = EasyConfig(self.eb_file)
+        deps = eb.dependencies()
+        self.assertEqual(len(deps), 2)
+        self.assertEqual(deps[0]['name'], 'second_build')
+        self.assertEqual(deps[1]['name'], 'first')
+
+        # more realistic example: only filter dep for POWER
+        self.contents = '\n'.join([
+            'easyblock = "ConfigureMake"',
+            'name = "pi"',
+            'version = "3.14"',
+            'versionsuffix = "-test"',
+            'homepage = "http://example.com"',
+            'description = "test easyconfig"',
+            'toolchain = {"name":"GCC", "version": "4.6.3"}',
+            'dependencies = ['
+            '   ("not_on_power", {"arch=*": "1.2.3", "arch=POWER": False}),',
+            ']',
+        ])
+        self.prep()
+
+        # only non-POWER arch, dependency is retained
+        for arch in (AARCH64, X86_64):
+            st.get_cpu_architecture = lambda: arch
+            eb = EasyConfig(self.eb_file)
+            deps = eb.dependencies()
+            self.assertEqual(len(deps), 1)
+            self.assertEqual(deps[0]['name'], 'not_on_power')
+
+        # only power, dependency gets filtered
+        st.get_cpu_architecture = lambda: POWER
+        eb = EasyConfig(self.eb_file)
+        deps = eb.dependencies()
+        self.assertEqual(deps, [])
+
     def test_extra_options(self):
         """ extra_options should allow other variables to be stored """
         init_config(build_options={'silent': True})
diff --git a/test/framework/systemtools.py b/test/framework/systemtools.py
index eba1625a17..3654882086 100644
--- a/test/framework/systemtools.py
+++ b/test/framework/systemtools.py
@@ -916,6 +916,24 @@ def test_pick_dep_version(self):
         error_pattern = "Unknown value type for version"
         self.assertErrorRegex(EasyBuildError, error_pattern, pick_dep_version, ('1.2.3', '4.5.6'))
 
+        # check support for using 'arch=*' as fallback key
+        dep_ver_dict = {
+            'arch=*': '1.2.3',
+            'arch=foo': '1.2.3-foo',
+            'arch=POWER': '1.2.3-ppc64le',
+        }
+        self.assertEqual(pick_dep_version(dep_ver_dict), '1.2.3-ppc64le')
+
+        del dep_ver_dict['arch=POWER']
+        self.assertEqual(pick_dep_version(dep_ver_dict), '1.2.3')
+
+        # check how faulty input is handled
+        self.assertErrorRegex(EasyBuildError, "Found empty dict as version!", pick_dep_version, {})
+        error_pattern = r"Unexpected keys in version: bar,foo \(only 'arch=' keys are supported\)"
+        self.assertErrorRegex(EasyBuildError, error_pattern, pick_dep_version, {'foo': '1.2', 'bar': '2.3'})
+        error_pattern = r"Unknown value type for version: .* \(1.23\), should be string value"
+        self.assertErrorRegex(EasyBuildError, error_pattern, pick_dep_version, 1.23)
+
     def test_check_os_dependency(self):
         """Test check_os_dependency."""