diff --git a/lib/spack/spack/solver/asp.py b/lib/spack/spack/solver/asp.py
index 7a8117976b..1b3eb8b1a8 100644
--- a/lib/spack/spack/solver/asp.py
+++ b/lib/spack/spack/solver/asp.py
@@ -716,6 +716,7 @@ def __init__(self, tests=False):
         self.variant_values_from_specs = set()
         self.version_constraints = set()
         self.target_constraints = set()
+        self.default_targets = {}
         self.compiler_version_constraints = set()
         self.post_facts = []
 
@@ -1164,7 +1165,7 @@ def preferred_variants(self, pkg_name):
                     pkg_name, variant.name, value
                 ))
 
-    def preferred_targets(self, pkg_name):
+    def target_preferences(self, pkg_name):
         key_fn = spack.package_prefs.PackagePrefs(pkg_name, 'target')
 
         if not self.target_specs_cache:
@@ -1175,13 +1176,25 @@ def preferred_targets(self, pkg_name):
 
         target_specs = self.target_specs_cache
         preferred_targets = [x for x in target_specs if key_fn(x) < 0]
-        if not preferred_targets:
-            return
 
-        preferred = preferred_targets[0]
-        self.gen.fact(fn.package_target_weight(
-            str(preferred.architecture.target), pkg_name, -30
-        ))
+        for i, preferred in enumerate(preferred_targets):
+            self.gen.fact(fn.package_target_weight(
+                str(preferred.architecture.target), pkg_name, i
+            ))
+
+        # generate weights for non-preferred targets on a per-package basis
+        default_targets = {
+            name: weight for
+            name, weight in self.default_targets.items()
+            if not any(preferred.architecture.target.name == name
+                       for preferred in preferred_targets)
+        }
+
+        num_preferred = len(preferred_targets)
+        for name, weight in default_targets.items():
+            self.gen.fact(fn.default_target_weight(
+                name, pkg_name, weight + num_preferred + 30
+            ))
 
     def flag_defaults(self):
         self.gen.h2("Compiler flag defaults")
@@ -1572,7 +1585,7 @@ def target_defaults(self, specs):
                 compiler.name, compiler.version, uarch.family.name
             ))
 
-        i = 0
+        i = 0  # TODO compute per-target offset?
         for target in candidate_targets:
             self.gen.fact(fn.target(target.name))
             self.gen.fact(fn.target_family(target.name, target.family.name))
@@ -1581,11 +1594,13 @@ def target_defaults(self, specs):
 
             # prefer best possible targets; weight others poorly so
             # they're not used unless set explicitly
+            # these are stored to be generated as facts later offset by the
+            # number of preferred targets
             if target.name in best_targets:
-                self.gen.fact(fn.default_target_weight(target.name, i))
+                self.default_targets[target.name] = i
                 i += 1
             else:
-                self.gen.fact(fn.default_target_weight(target.name, 100))
+                self.default_targets[target.name] = 100
 
             self.gen.newline()
 
@@ -1862,7 +1877,7 @@ def setup(self, driver, specs, reuse=None):
             self.pkg_rules(pkg, tests=self.tests)
             self.gen.h2('Package preferences: %s' % pkg)
             self.preferred_variants(pkg)
-            self.preferred_targets(pkg)
+            self.target_preferences(pkg)
 
         # Inject dev_path from environment
         env = ev.active_environment()
diff --git a/lib/spack/spack/solver/concretize.lp b/lib/spack/spack/solver/concretize.lp
index b9b3141499..5ee2eeb731 100644
--- a/lib/spack/spack/solver/concretize.lp
+++ b/lib/spack/spack/solver/concretize.lp
@@ -779,10 +779,13 @@ target_compatible(Descendent, Ancestor)
 #defined target_satisfies/2.
 #defined target_parent/2.
 
-% The target weight is either the default target weight
-% or a more specific per-package weight if set
+% If the package does not have any specific weight for this
+% target, offset the default weights by the number of specific
+% weights and use that. We additionally offset by 30 to ensure
+% preferences are propagated even against large numbers of
+% otherwise "better" matches.
 target_weight(Target, Package, Weight)
-  :- default_target_weight(Target, Weight),
+  :- default_target_weight(Target, Package, Weight),
      node(Package),
      not derive_target_from_parent(_, Package),
      not package_target_weight(Target, Package, _).
@@ -1238,7 +1241,7 @@ opt_criterion(1, "non-preferred targets").
 %-----------------
 #heuristic version(Package, Version) : version_declared(Package, Version, 0), node(Package). [10, true]
 #heuristic version_weight(Package, 0) : version_declared(Package, Version, 0), node(Package). [10, true]
-#heuristic node_target(Package, Target) : default_target_weight(Target, 0), node(Package). [10, true]
+#heuristic node_target(Package, Target) : package_target_weight(Target, Package, 0), node(Package). [10, true]
 #heuristic node_target_weight(Package, 0) : node(Package). [10, true]
 #heuristic variant_value(Package, Variant, Value) : variant_default_value(Package, Variant, Value), node(Package). [10, true]
 #heuristic provider(Package, Virtual) : possible_provider_weight(Package, Virtual, 0, _), virtual_node(Virtual). [10, true]
diff --git a/lib/spack/spack/test/concretize_preferences.py b/lib/spack/spack/test/concretize_preferences.py
index 525bd0701f..28bb13ee22 100644
--- a/lib/spack/spack/test/concretize_preferences.py
+++ b/lib/spack/spack/test/concretize_preferences.py
@@ -144,7 +144,7 @@ def test_preferred_target(self, mutable_mock_repo):
 
         update_packages('mpileaks', 'target', [default])
         spec = concretize('mpileaks')
-        assert str(spec['mpich'].target) == default
+        assert str(spec['mpileaks'].target) == default
         assert str(spec['mpich'].target) == default
 
     def test_preferred_versions(self):