diff --git a/README.rst b/README.rst
index adde47078..9f883ed8c 100644
--- a/README.rst
+++ b/README.rst
@@ -267,8 +267,8 @@ First, compile ``requirements.txt`` as usual:
     #
     #    pip-compile
     #
-    django==2.1.12
-    pytz==2019.2              # via django
+    django==2.1.15
+    pytz==2019.3              # via django
 
 Now compile the dev requirements and the ``requirements.txt`` file is used as
 a constraint:
@@ -282,8 +282,9 @@ a constraint:
     #
     #    pip-compile dev-requirements.in
     #
-    django-debug-toolbar==2.0
-    django==2.1.12            # via django-debug-toolbar
+    django-debug-toolbar==2.1
+    django==2.1.15            # via django-debug-toolbar
+    pytz==2019.3              # via django
     sqlparse==0.3.0           # via django-debug-toolbar
 
 As you can see above, even though a ``2.2`` release of Django is available, the
diff --git a/piptools/resolver.py b/piptools/resolver.py
index 7473d4bd6..88631c263 100644
--- a/piptools/resolver.py
+++ b/piptools/resolver.py
@@ -332,6 +332,17 @@ def _iter_dependencies(self, ireq):
         Editable requirements will never be looked up, as they may have
         changed at any time.
         """
+        # Pip does not resolve dependencies of constraints. We skip handling
+        # constraints here as well to prevent the cache from being polluted.
+        # Constraints that are later determined to be dependencies will be
+        # marked as non-constraints in later rounds by
+        # `combine_install_requirements`, and will be properly resolved.
+        # See https://github.com/pypa/pip/
+        # blob/6896dfcd831330c13e076a74624d95fa55ff53f4/src/pip/_internal/
+        # legacy_resolve.py#L325
+        if ireq.constraint:
+            return
+
         if ireq.editable or is_url_requirement(ireq):
             for dependency in self.repository.get_dependencies(ireq):
                 yield dependency
diff --git a/tests/test_cli_compile.py b/tests/test_cli_compile.py
index 0cf552283..fd6ba7b0f 100644
--- a/tests/test_cli_compile.py
+++ b/tests/test_cli_compile.py
@@ -1016,3 +1016,27 @@ def test_remove_outdated_options(runner, input_opts, output_opts):
 
     assert out.exit_code == 0, out
     assert out.stderr.strip() == input_opts
+
+
+def test_sub_dependencies_with_constraints(pip_conf, runner):
+    # Write constraints file
+    with open("constraints.txt", "w") as constraints_in:
+        constraints_in.write("small-fake-a==0.1\n")
+        constraints_in.write("small-fake-b==0.2\n")
+        constraints_in.write("small-fake-with-unpinned-deps==0.1")
+
+    with open("requirements.in", "w") as req_in:
+        req_in.write("-c constraints.txt\n")
+        req_in.write("small_fake_with_deps_and_sub_deps")  # require fake package
+
+    out = runner.invoke(cli)
+
+    assert out.exit_code == 0
+
+    req_out_lines = set(out.stderr.splitlines())
+    assert {
+        "small-fake-a==0.1         # via small-fake-with-unpinned-deps",
+        "small-fake-b==0.2         # via small-fake-with-unpinned-deps",
+        "small-fake-with-deps-and-sub-deps==0.1",
+        "small-fake-with-unpinned-deps==0.1  # via small-fake-with-deps-and-sub-deps",
+    }.issubset(req_out_lines)
diff --git a/tests/test_data/fake-index.json b/tests/test_data/fake-index.json
index df64009ef..5c5d76677 100644
--- a/tests/test_data/fake-index.json
+++ b/tests/test_data/fake-index.json
@@ -1,4 +1,7 @@
 {
+  "aiohttp": {
+    "3.6.2": {"": ["yarl"]}
+  },
   "anyjson": {
     "0.3.3": {"": []}
   },
@@ -79,6 +82,9 @@
       "setuptools>=18.5"
     ]}
   },
+  "idna": {
+    "2.8": {"": []}
+  },
   "ipython": {
     "2.1.0": {
       "": ["gnureadline"],
@@ -163,5 +169,8 @@
     "0.6": {"": []},
     "0.10": {"": []},
     "0.10.4": {"": []}
+  },
+  "yarl": {
+    "1.4.2": {"": ["idna"]}
   }
 }
diff --git a/tests/test_data/minimal_wheels/small_fake_with_deps_and_sub_deps-0.1-py2.py3-none-any.whl b/tests/test_data/minimal_wheels/small_fake_with_deps_and_sub_deps-0.1-py2.py3-none-any.whl
new file mode 100644
index 000000000..d611277c0
Binary files /dev/null and b/tests/test_data/minimal_wheels/small_fake_with_deps_and_sub_deps-0.1-py2.py3-none-any.whl differ
diff --git a/tests/test_data/packages/small_fake_with_deps_and_sub_deps/setup.py b/tests/test_data/packages/small_fake_with_deps_and_sub_deps/setup.py
new file mode 100644
index 000000000..bff3d6bac
--- /dev/null
+++ b/tests/test_data/packages/small_fake_with_deps_and_sub_deps/setup.py
@@ -0,0 +1,7 @@
+from setuptools import setup
+
+setup(
+    name="small_fake_with_deps_and_sub_deps",
+    version=0.1,
+    install_requires=["small-fake-with-unpinned-deps"],
+)
diff --git a/tests/test_resolver.py b/tests/test_resolver.py
index 97792ac4c..91cd5248a 100644
--- a/tests/test_resolver.py
+++ b/tests/test_resolver.py
@@ -172,6 +172,11 @@
                     "pytz==2016.4 (from celery==4.0.2)",
                 ],
             ),
+            # Check that dependencies of relevant constraints are resolved
+            (
+                ["aiohttp", ("yarl==1.4.2", True)],
+                ["aiohttp==3.6.2", "idna==2.8 (from yarl==1.4.2)", "yarl==1.4.2"],
+            ),
         ]
     ),
 )
@@ -253,6 +258,19 @@ def test_iter_dependencies(resolver, from_line):
         next(res._iter_dependencies(ireq))
 
 
+def test_iter_dependencies_results(resolver, from_line):
+    res = resolver([])
+    ireq = from_line("aiohttp==3.6.2")
+    assert next(res._iter_dependencies(ireq)).comes_from == ireq
+
+
+def test_iter_dependencies_ignores_constraints(resolver, from_line):
+    res = resolver([])
+    ireq = from_line("aiohttp==3.6.2", constraint=True)
+    with pytest.raises(StopIteration):
+        next(res._iter_dependencies(ireq))
+
+
 def test_combine_install_requirements(from_line):
     celery30 = from_line("celery>3.0", comes_from="-r requirements.in")
     celery31 = from_line("celery==3.1.1", comes_from=from_line("fake-package"))