diff --git a/niceman/distributions/debian.py b/niceman/distributions/debian.py
index 007bee803..a88739430 100644
--- a/niceman/distributions/debian.py
+++ b/niceman/distributions/debian.py
@@ -13,6 +13,8 @@
 import attr
 from collections import defaultdict
 
+from six.moves import map
+
 import pytz
 
 from niceman import utils
@@ -89,8 +91,24 @@ class DEBPackage(Package):
     versions = attr.ib(default=None)  # Hash ver_str -> [Array of source names]
     install_date = attr.ib(default=None)
     files = attr.ib(default=attr.Factory(list))
-_register_with_representer(DEBPackage)
 
+    def satisfies(self, other):
+        """return True if this package (self) satisfies the requirements of 
+        the passed package (other)"""
+        if not isinstance(other, Package):
+            raise TypeError('satisfies() requires a package argument')
+        if not isinstance(other, DEBPackage):
+            return False
+        if self.name != other.name:
+            return False
+        if other.version is not None and self.version != other.version:
+            return False
+        if other.architecture is not None \
+                and self.architecture != other.architecture:
+            return False
+        return True
+
+_register_with_representer(DEBPackage)
 
 @attr.s
 class DebianDistribution(Distribution):
@@ -153,6 +171,31 @@ def normalize(self):
         #   would make us require supporting flexible typing -- string or a list
         pass
 
+    def satisfies_package(self, package):
+        """return True if this distribution (self) satisfies the requirements 
+        of the passed package"""
+        if not isinstance(package, Package):
+            raise TypeError('satisfies_package() requires a package argument')
+        if not isinstance(package, DEBPackage):
+            return False
+        return any([ p.satisfies(package) for p in self.packages ])
+
+    def satisfies(self, other):
+        """return True if this distribution (self) satisfies the requirements 
+        of the other distribution (other)"""
+        if not isinstance(other, Distribution):
+            raise TypeError('satisfies() requires a distribution argument')
+        if not isinstance(other, DebianDistribution):
+            return False
+        return all(map(self.satisfies_package, other.packages))
+
+    def __sub__(self, other):
+        # the semantics of distribution subtraction are, for d1 - d2:
+        #     what is specified in d1 that is not specified in d2
+        #     or how does d2 fall short of d1
+        #     or what is in d1 that isn't satisfied by d2
+        return [ p for p in self.packages if not other.satisfies_package(p) ]
+
     # to grow:
     #  def __iadd__(self, another_instance or DEBPackage, or APTSource)
     #  def __add__(self, another_instance or DEBPackage, or APTSource)
diff --git a/niceman/distributions/tests/test_debian.py b/niceman/distributions/tests/test_debian.py
index a4228db2c..a2c6a4bd6 100644
--- a/niceman/distributions/tests/test_debian.py
+++ b/niceman/distributions/tests/test_debian.py
@@ -12,6 +12,10 @@
 from pprint import pprint
 
 from niceman.distributions.debian import DebTracer
+from niceman.distributions.debian import DEBPackage
+from niceman.distributions.debian import DebianDistribution
+
+import pytest
 
 import mock
 
@@ -132,4 +136,67 @@ def _run_dpkg_query(subfiles):
         '/usr/bin/fail2ban-server': {'name': u'fail2ban'},
         '/usr/lib/afni/bin/afni': {'name': u'afni'},
         '/bin/sh': {'name': u'dash'}
-    }
\ No newline at end of file
+    }
+
+@pytest.fixture
+def setup_packages():
+    """set up the package comparison tests"""
+    a = DEBPackage(name='p1')
+    b = DEBPackage(name='p1', version='1.0')
+    c = DEBPackage(name='p1', version='1.1')
+    d = DEBPackage(name='p1', architecture='i386')
+    e = DEBPackage(name='p1', architecture='alpha')
+    f = DEBPackage(name='p1', version='1.1', architecture='i386')
+    g = DEBPackage(name='p2')
+    return (a, b, c, d, e, f, g)
+
+def test_package_satisfies(setup_packages):
+    (p1, p1v10, p1v11, p1ai, p1aa, p1v11ai, p2) = setup_packages
+    assert p1.satisfies(p1)
+    assert p1v10.satisfies(p1v10)
+    assert not p1.satisfies(p1v10)
+    assert p1v10.satisfies(p1)
+    assert not p1v10.satisfies(p1v11)
+    assert not p1.satisfies(p2)
+    assert not p1v10.satisfies(p2)
+    assert not p2.satisfies(p1v10)
+    assert not p1v10.satisfies(p1aa)
+    assert p1aa.satisfies(p1)
+    assert not p1aa.satisfies(p1v10)
+    assert not p1aa.satisfies(p1ai)
+    assert not p1v11.satisfies(p1v11ai)
+    assert p1v11ai.satisfies(p1v11)
+
+@pytest.fixture
+def setup_distributions():
+    (p1, p1v10, p1v11, p1ai, p1aa, p1v11ai, p2) = setup_packages()
+    d1 = DebianDistribution(name='debian 1')
+    d1.packages = [p1]
+    d2 = DebianDistribution(name='debian 2')
+    d2.packages = [p1v11]
+    return (d1, d2)
+
+def test_distribution_satisfies_package(setup_distributions, setup_packages):
+    (d1, d2) = setup_distributions
+    (p1, p1v10, p1v11, p1ai, p1aa, p1v11ai, p2) = setup_packages
+    assert d1.satisfies_package(p1)
+    assert not d1.satisfies_package(p1v10)
+    assert d2.satisfies_package(p1)
+    assert not d2.satisfies_package(p1v10)
+    assert d2.satisfies_package(p1v11)
+
+def test_distribution_statisfies(setup_distributions):
+    (d1, d2) = setup_distributions
+    assert not d1.satisfies(d2)
+    assert d2.satisfies(d1)
+
+def test_distribution_sub():
+    (p1, p1v10, p1v11, p1ai, p1aa, p1v11ai, p2) = setup_packages()
+    d1 = DebianDistribution(name='debian 1')
+    d1.packages = [p1, p2]
+    d2 = DebianDistribution(name='debian 2')
+    d2.packages = [p1v11, p2]
+    assert d1-d2 == []
+    result = d2-d1
+    assert len(result) == 1
+    assert result[0] == p1v11