diff --git a/conda/core/index.py b/conda/core/index.py
index a6c81504330..25dc634b7ea 100644
--- a/conda/core/index.py
+++ b/conda/core/index.py
@@ -4,6 +4,7 @@
 from __future__ import absolute_import, division, print_function, unicode_literals
 
 import os
+import re
 from itertools import chain
 from logging import getLogger
 import platform
@@ -172,11 +173,17 @@ def _supplement_index_with_system(index):
     libc_family, libc_version = context.libc_family_version
     is_linux = context.subdir.startswith("linux-")
     if is_linux:
+        # By convention, the kernel release string should be three or four
+        # numeric components, separated by dots, followed by vendor-specific
+        # bits.  For the purposes of versioning the `__linux` virtual package,
+        # discard everything after the last digit of the third or fourth
+        # numeric component; note that this breaks version ordering for
+        # development (`-rcN`) kernels, but we'll deal with that later.
         dist_version = os.environ.get('CONDA_OVERRIDE_LINUX', context.platform_system_release[1])
-        if '-' in dist_version:
-            dist_version = dist_version.split('-')[0]
-        rec = _make_virtual_package('__linux', dist_version)
+        m = re.match(r'\d+\.\d+(\.\d+)?(\.\d+)?', dist_version)
+        rec = _make_virtual_package('__linux', m.group() if m else "0")
         index[rec] = rec
+
         if not (libc_family and libc_version):
             # Default to glibc when using CONDA_SUBDIR var
             libc_family = "glibc"
diff --git a/tests/core/test_index.py b/tests/core/test_index.py
index 81b4d2d4d32..465ac3f568e 100644
--- a/tests/core/test_index.py
+++ b/tests/core/test_index.py
@@ -66,25 +66,25 @@ def test_supplement_index_with_system_osx():
 
 
 @pytest.mark.skipif(not on_linux, reason="linux-only test")
-def test_supplement_index_with_system_linux():
-      index = {}
-      with env_vars({'CONDA_OVERRIDE_LINUX': '4.2.0'}):
-          _supplement_index_with_system(index)
-
-      linux_pkg = next(iter(_ for _ in index if _.name == '__linux'))
-      assert linux_pkg.version == '4.2.0'
-      assert linux_pkg.package_type == PackageType.VIRTUAL_SYSTEM
-
-
-@pytest.mark.skipif(not on_linux, reason="linux-only test")
-def test_supplement_index_with_system_linux_extended():
-      index = {}
-      with env_vars({'CONDA_OVERRIDE_LINUX': '4.2.0-42-generic'}):
-          _supplement_index_with_system(index)
+@pytest.mark.parametrize("release_str,version", [
+        ("1.2.3.4", "1.2.3.4"), # old numbering system
+        ("4.2", "4.2"),
+        ("4.2.1", "4.2.1"),
+        ("4.2.0-42-generic", "4.2.0"),
+        ("5.4.89+", "5.4.89"),
+        ("5.5-rc1", "5.5"),
+        ("9.1.a", "9.1"),       # should probably be "0"
+        ("9.1.a.2", "9.1"),     # should probably be "0"
+        ("9.a.1", "0"),
+    ])
+def test_supplement_index_with_system_linux(release_str, version):
+    index = {}
+    with env_vars({'CONDA_OVERRIDE_LINUX': release_str}):
+        _supplement_index_with_system(index)
 
-      linux_pkg = next(iter(_ for _ in index if _.name == '__linux'))
-      assert linux_pkg.version == '4.2.0'
-      assert linux_pkg.package_type == PackageType.VIRTUAL_SYSTEM
+    linux_pkg = next(iter(_ for _ in index if _.name == '__linux'))
+    assert linux_pkg.version == version
+    assert linux_pkg.package_type == PackageType.VIRTUAL_SYSTEM
 
 
 @pytest.mark.skipif(on_win or on_mac, reason="linux-only test")