diff --git a/piptools/resolver.py b/piptools/resolver.py
index f9d3d1250..3fa736c6d 100644
--- a/piptools/resolver.py
+++ b/piptools/resolver.py
@@ -206,6 +206,7 @@ def __init__(
         prereleases: Optional[bool] = False,
         clear_caches: bool = False,
         allow_unsafe: bool = False,
+        cuts: Optional[Set[str]] = None,
     ) -> None:
         """
         This class resolves a given set of constraints (a collection of
@@ -220,6 +221,7 @@ def __init__(
         self.clear_caches = clear_caches
         self.allow_unsafe = allow_unsafe
         self.unsafe_constraints: Set[InstallRequirement] = set()
+        self.cuts = cuts or set()
 
         options = self.repository.options
         if "legacy-resolver" not in options.deprecated_features_enabled:
@@ -353,7 +355,14 @@ def _resolve_one_round(self) -> Tuple[bool, Set[InstallRequirement]]:
         their_constraints: List[InstallRequirement] = []
         with log.indentation():
             for best_match in best_matches:
-                their_constraints.extend(self._iter_dependencies(best_match))
+                for dep in self._iter_dependencies(best_match):
+                    # Must iterate even if we're going to cut all dependencies,
+                    # so our dependency cache gets populated.
+                    pair = f"{best_match.name}:{dep.name}"
+                    if best_match.name in self.cuts or pair in self.cuts:
+                        log.debug(f"Cutting dependency {pair}")
+                    else:
+                        their_constraints.append(dep)
         # Grouping constraints to make clean diff between rounds
         theirs = set(self._group_constraints(their_constraints))
 
diff --git a/piptools/scripts/compile.py b/piptools/scripts/compile.py
index 0c98c6b2d..3f6134e17 100755
--- a/piptools/scripts/compile.py
+++ b/piptools/scripts/compile.py
@@ -245,6 +245,13 @@ def _get_default_option(option_name: str) -> Any:
     default=True,
     help="Add options to generated file",
 )
+@click.option(
+    "--cut-deps",
+    multiple=True,
+    help="Ignore a package's dependencies. May be used more than once. "
+    "Pass just the package name to ignore all of its dependencies. "
+    "Pass pkg-name:dep-name to ignore just one dependency.",
+)
 def cli(
     ctx: click.Context,
     verbose: int,
@@ -279,6 +286,7 @@ def cli(
     resolver_name: str,
     emit_index_url: bool,
     emit_options: bool,
+    cut_deps: Tuple[str, ...],
 ) -> None:
     """Compiles requirements.txt from requirements.in specs."""
     log.verbosity = verbose - quiet
@@ -483,6 +491,7 @@ def cli(
             cache=DependencyCache(cache_dir),
             clear_caches=rebuild,
             allow_unsafe=allow_unsafe,
+            cuts=set(cut_deps),
         )
         results = resolver.resolve(max_rounds=max_rounds)
         hashes = resolver.resolve_hashes(results) if generate_hashes else None
diff --git a/tests/test_resolver.py b/tests/test_resolver.py
index 0e9b2fef1..6c8e8c0c5 100644
--- a/tests/test_resolver.py
+++ b/tests/test_resolver.py
@@ -250,6 +250,81 @@ def test_resolver__allows_unsafe_deps(
     assert output == {str(line) for line in expected}
 
 
+@pytest.mark.parametrize(
+    (
+        "input",
+        "cuts",
+        "expected",
+    ),
+    (
+        # No cuts, get all recursive dependencies.
+        (
+            ["flask==0.10.1"],
+            set(),
+            {
+                'markupsafe==0.23 (from jinja2==2.7.3->flask==0.10.1)',
+                'itsdangerous==0.24 (from flask==0.10.1)',
+                'werkzeug==0.10.4 (from flask==0.10.1)',
+                'flask==0.10.1',
+                'jinja2==2.7.3 (from flask==0.10.1)',
+            },
+        ),
+        # Cut all of flask's dependencies. Get only flask.
+        (
+            ["flask==0.10.1"],
+            {"flask"},
+            {
+                'flask==0.10.1',
+            },
+        ),
+        # Cut flask's dependency on Jinja2. Get the remaining dependencies.
+        (
+            ["flask==0.10.1"],
+            {"flask:Jinja2"},
+            {
+                'itsdangerous==0.24 (from flask==0.10.1)',
+                'werkzeug==0.10.4 (from flask==0.10.1)',
+                'flask==0.10.1',
+            },
+        ),
+        # Again cut flask's dependency on Jinja2, but now also install another
+        # package that depends on Jinja2. Now we do get Jinja2, among others.
+        (
+            ["flask==0.10.1", "ipython[notebook]==2.1.0"],
+            {"flask:Jinja2"},
+            {
+                'jinja2==2.7.3 (from ipython[notebook]==2.1.0)',
+                'tornado==3.2.2 (from ipython[notebook]==2.1.0)',
+                'itsdangerous==0.24 (from flask==0.10.1)',
+                'markupsafe==0.23 (from jinja2==2.7.3->ipython[notebook]==2.1.0)',
+                'pyzmq==2.1.12 (from ipython[notebook]==2.1.0)',
+                'ipython[notebook]==2.1.0',
+                'gnureadline==6.3.3 (from ipython[notebook]==2.1.0)',
+                'flask==0.10.1',
+                'werkzeug==0.10.4 (from flask==0.10.1)',
+            },
+        ),
+    ),
+)
+def test_resolver__cut_deps(
+    resolver,
+    from_line,
+    input,
+    cuts,
+    expected,
+):
+    input = [line if isinstance(line, tuple) else (line, False) for line in input]
+    input = [from_line(req[0], constraint=req[1]) for req in input]
+    resolver = resolver(
+        input,
+        cuts=cuts,
+    )
+    output = resolver.resolve()
+    output = {str(line) for line in output}
+
+    assert output == expected
+
+
 def test_resolver__max_number_rounds_reached(resolver, from_line):
     """
     Resolver should raise an exception if max round has been reached.