diff --git a/easybuild/tools/modules.py b/easybuild/tools/modules.py
index bdac20c274..8df257fa90 100644
--- a/easybuild/tools/modules.py
+++ b/easybuild/tools/modules.py
@@ -1283,14 +1283,14 @@ def tweak_stdout(txt):
 
         return super(EnvironmentModulesTcl, self).run_module(*args, **kwargs)
 
-    def available(self, mod_name=None):
+    def available(self, mod_name=None, extra_args=None):
         """
         Return a list of available modules for the given (partial) module name;
         use None to obtain a list of all available modules.
 
         :param mod_name: a (partial) module name for filtering (default: None)
         """
-        mods = super(EnvironmentModulesTcl, self).available(mod_name=mod_name)
+        mods = super(EnvironmentModulesTcl, self).available(mod_name=mod_name, extra_args=extra_args)
         # strip off slash at beginning, if it's there
         # under certain circumstances, 'modulecmd.tcl avail' (DEISA variant) spits out available modules like this
         clean_mods = [mod.lstrip(os.path.sep) for mod in mods]
@@ -1328,6 +1328,8 @@ class EnvironmentModules(EnvironmentModulesTcl):
     MAX_VERSION = None
     VERSION_REGEXP = r'^Modules\s+Release\s+(?P<version>\d[^+\s]*)(\+\S*)?\s'
 
+    SHOW_HIDDEN_OPTION = '--all'
+
     def __init__(self, *args, **kwargs):
         """Constructor, set Environment Modules-specific class variable values."""
         # ensure in-depth modulepath search (MODULES_AVAIL_INDEPTH has been introduced in v4.3)
@@ -1383,6 +1385,21 @@ def check_module_output(self, cmd, stdout, stderr):
         else:
             self.log.debug("No errors detected when running module command '%s'", cmd)
 
+    def available(self, mod_name=None, extra_args=None):
+        """
+        Return a list of available modules for the given (partial) module name;
+        use None to obtain a list of all available modules.
+
+        :param mod_name: a (partial) module name for filtering (default: None)
+        """
+        if extra_args is None:
+            extra_args = []
+        # make hidden modules visible (requires Environment Modules 4.6.0)
+        if StrictVersion(self.version) >= StrictVersion('4.6.0'):
+            extra_args.append(self.SHOW_HIDDEN_OPTION)
+
+        return super(EnvironmentModules, self).available(mod_name=mod_name, extra_args=extra_args)
+
     def get_setenv_value_from_modulefile(self, mod_name, var_name):
         """
         Get value for specific 'setenv' statement from module file for the specified module.
diff --git a/test/framework/modules.py b/test/framework/modules.py
index c2460c7a11..2a05395b7c 100644
--- a/test/framework/modules.py
+++ b/test/framework/modules.py
@@ -218,6 +218,12 @@ def test_avail(self):
             self.assertIn('bzip2/.1.0.6', ms)
             self.assertIn('toy/.0.0-deps', ms)
             self.assertIn('OpenMPI/.2.1.2-GCC-6.4.0-2.28', ms)
+        elif (isinstance(self.modtool, EnvironmentModules)
+                and StrictVersion(self.modtool.version) >= StrictVersion('4.6.0')):
+            # bzip2/.1.0.6 is not there, since that's a module file in Lua syntax
+            self.assertEqual(len(ms), TEST_MODULES_COUNT + 2)
+            self.assertIn('toy/.0.0-deps', ms)
+            self.assertIn('OpenMPI/.2.1.2-GCC-6.4.0-2.28', ms)
         else:
             self.assertEqual(len(ms), TEST_MODULES_COUNT)