diff --git a/src/python/pants/python/BUILD b/src/python/pants/python/BUILD
index 8babb0c9236..e839d3fd64a 100644
--- a/src/python/pants/python/BUILD
+++ b/src/python/pants/python/BUILD
@@ -21,6 +21,7 @@ python_library(
 
 python_tests(
   name='tests',
+  sources=['*_test.py', '!*_integration.py'],
   dependencies=[
     '3rdparty/python:pex',
     ':python',
@@ -33,3 +34,16 @@ python_tests(
   ],
   tags = {'partially_type_checked'},
 )
+
+
+python_tests(
+  name='integration',
+  sources=['*_integration.py'],
+  dependencies=[
+    '3rdparty/python:pex',
+    'src/python/pants/util:contextutil',
+    'src/python/pants/testutil:int-test',
+    'testprojects/src/python:python_targets_directory',
+  ],
+  tags = {'integration', 'partially_type_checked'},
+)
diff --git a/src/python/pants/python/pex_build_util.py b/src/python/pants/python/pex_build_util.py
index 1dcd595c96f..fef27427353 100644
--- a/src/python/pants/python/pex_build_util.py
+++ b/src/python/pants/python/pex_build_util.py
@@ -9,7 +9,7 @@
 from typing import Callable, Dict, List, Optional, Sequence, Set, Tuple
 
 from pex.fetcher import Fetcher
-from pex.interpreter import PythonInterpreter
+from pex.interpreter import PythonIdentity, PythonInterpreter
 from pex.pex_builder import PEXBuilder
 from pex.pex_info import PexInfo
 from pex.platforms import Platform
@@ -449,14 +449,23 @@ def _prepare_inits(self) -> Set[str]:
     def set_emit_warnings(self, emit_warnings):
         self._builder.info.emit_warnings = emit_warnings
 
+    def _set_major_minor_interpreter_constraint_for_ipex(
+        self, info: PexInfo, identity: PythonIdentity,
+    ) -> PexInfo:
+        interpreter_name = identity.requirement.name
+        major, minor, _patch = identity.version
+        major_minor_only_constraint = f"{interpreter_name}=={major}.{minor}.*"
+        return ipex_launcher.modify_pex_info(
+            info, interpreter_constraints=[str(major_minor_only_constraint)]
+        )
+
     def _shuffle_underlying_pex_builder(self) -> Tuple[PexInfo, Path]:
         """Replace the original builder with a new one, and just pull files from the old chroot."""
         # Ensure that (the interpreter selected to resolve requirements when the ipex is first run) is
         # (the exact same interpreter we used to resolve those requirements here). This is the only (?)
         # way to ensure that the ipex bootstrap uses the *exact* same interpreter version.
-        self._builder.info = ipex_launcher.modify_pex_info(
-            self._builder.info,
-            interpreter_constraints=[str(self._builder.interpreter.identity.requirement)],
+        self._builder.info = self._set_major_minor_interpreter_constraint_for_ipex(
+            self._builder.info, self._builder.interpreter.identity
         )
 
         orig_info = self._builder.info.copy()
@@ -465,6 +474,9 @@ def _shuffle_underlying_pex_builder(self) -> Tuple[PexInfo, Path]:
 
         # Mutate the PexBuilder object which is manipulated by this subsystem.
         self._builder = PEXBuilder(interpreter=self._builder.interpreter)
+        self._builder.info = self._set_major_minor_interpreter_constraint_for_ipex(
+            self._builder.info, self._builder.interpreter.identity
+        )
 
         return (orig_info, Path(orig_chroot.path()))
 
diff --git a/src/python/pants/python/pex_build_util_test_integration.py b/src/python/pants/python/pex_build_util_test_integration.py
new file mode 100644
index 00000000000..2450bf79d62
--- /dev/null
+++ b/src/python/pants/python/pex_build_util_test_integration.py
@@ -0,0 +1,50 @@
+# Copyright 2020 Pants project contributors (see CONTRIBUTORS.md).
+# Licensed under the Apache License, Version 2.0 (see LICENSE).
+
+import json
+import os
+import subprocess
+
+from pex.interpreter import PythonInterpreter
+
+from pants.testutil.pants_run_integration_test import PantsRunIntegrationTest
+from pants.util.collections import assert_single_element
+from pants.util.contextutil import open_zip, temporary_dir
+
+
+class PexBuildUtilIntegrationTest(PantsRunIntegrationTest):
+
+    binary_target_address = "testprojects/src/python/python_targets:test"
+
+    def test_ipex_gets_imprecise_constraint(self) -> None:
+        cur_interpreter_id = PythonInterpreter.get().identity
+        interpreter_name = cur_interpreter_id.requirement.name
+        major, minor, patch = cur_interpreter_id.version
+
+        # Pin the selected interpreter to the one used by pants to execute this test.
+        cur_interpreter_constraint = f"{interpreter_name}=={major}.{minor}.{patch}"
+
+        # Validate the the .ipex file specifically matches the major and minor versions, but allows
+        # any patch version.
+        imprecise_constraint = f"{interpreter_name}=={major}.{minor}.*"
+
+        with temporary_dir() as tmp_dir:
+            self.do_command(
+                "--binary-py-generate-ipex",
+                "binary",
+                self.binary_target_address,
+                config={
+                    "GLOBAL": {"pants_distdir": tmp_dir},
+                    "python-setup": {"interpreter_constraints": [cur_interpreter_constraint],},
+                },
+            )
+
+            pex_path = os.path.join(tmp_dir, "test.ipex")
+            assert os.path.isfile(pex_path)
+            pex_execution_result = subprocess.run([pex_path], stdout=subprocess.PIPE, check=True)
+            assert pex_execution_result.stdout.decode() == "test!\n"
+
+            with open_zip(pex_path) as zf:
+                info = json.loads(zf.read("PEX-INFO"))
+                constraint = assert_single_element(info["interpreter_constraints"])
+                assert constraint == imprecise_constraint