diff --git a/lib/spack/spack/solver/concretize.lp b/lib/spack/spack/solver/concretize.lp
index b27b80dc6e..d012bc3cf3 100644
--- a/lib/spack/spack/solver/concretize.lp
+++ b/lib/spack/spack/solver/concretize.lp
@@ -537,9 +537,6 @@ root(Dependency, 1) :- not root(Dependency), node(Dependency).
     1@8,Package,Variant,Value
     : variant_not_default(Package, Variant, Value, Weight), not root(Package)
 }.
-#minimize{
-    Weight@8,Package : version_weight(Package, Weight)
-}.
 
 % Try to maximize the number of compiler matches in the DAG,
 % while minimizing the number of nodes. This is done because
@@ -548,10 +545,15 @@ root(Dependency, 1) :- not root(Dependency), node(Dependency).
 #minimize{ 1@7,Package : node(Package) }.
 #maximize{ Weight@7,Package : compiler_version_match(Package, Weight) }.
 
+% Choose more recent versions for nodes
+#minimize{
+    Weight@6,Package : version_weight(Package, Weight)
+}.
+
 % Try to use preferred compilers
-#minimize{ Weight@6,Package : compiler_weight(Package, Weight) }.
+#minimize{ Weight@5,Package : compiler_weight(Package, Weight) }.
 
 % Maximize the number of matches for targets in the DAG, try
 % to select the preferred target.
-#maximize{ Weight@5,Package : node_target_match(Package, Weight) }.
-#minimize{ Weight@4,Package : node_target_weight(Package, Weight) }.
+#maximize{ Weight@4,Package : node_target_match(Package, Weight) }.
+#minimize{ Weight@3,Package : node_target_weight(Package, Weight) }.
diff --git a/lib/spack/spack/test/concretize.py b/lib/spack/spack/test/concretize.py
index 8640c91a9e..11c2764822 100644
--- a/lib/spack/spack/test/concretize.py
+++ b/lib/spack/spack/test/concretize.py
@@ -923,3 +923,18 @@ def test_activating_test_dependencies(
             msg = "Test dependency in package '{0}' is unexpected"
             node = s[pkg_name]
             assert not node.dependencies(deptype='test'), msg.format(pkg_name)
+
+    @pytest.mark.regression('20019')
+    def test_compiler_match_is_preferred_to_newer_version(self):
+        if spack.config.get('config:concretizer') == 'original':
+            pytest.xfail('Known failure of the original concretizer')
+
+        # This spec depends on openblas. Openblas has a conflict
+        # that doesn't allow newer versions with gcc@4.4.0. Check
+        # that an old version of openblas is selected, rather than
+        # a different compiler for just that node.
+        spec_str = 'simple-inheritance+openblas %gcc@4.4.0 os=redhat6'
+        s = Spec(spec_str).concretized()
+
+        assert 'openblas@0.2.13' in s
+        assert s['openblas'].satisfies('%gcc@4.4.0')
diff --git a/lib/spack/spack/test/data/config/compilers.yaml b/lib/spack/spack/test/data/config/compilers.yaml
index 3a2db05e72..3a63796941 100644
--- a/lib/spack/spack/test/data/config/compilers.yaml
+++ b/lib/spack/spack/test/data/config/compilers.yaml
@@ -102,6 +102,15 @@ compilers:
       cxxflags: -O0 -g
       fflags: -O0 -g
     modules: 'None'
+- compiler:
+    spec: gcc@4.4.0
+    operating_system: redhat6
+    paths:
+      cc: /path/to/gcc440
+      cxx: /path/to/g++440
+      f77: /path/to/gfortran440
+      fc: /path/to/gfortran440
+    modules: 'None'
 - compiler:
     spec: clang@3.5
     operating_system: redhat6
diff --git a/var/spack/repos/builtin.mock/packages/openblas/package.py b/var/spack/repos/builtin.mock/packages/openblas/package.py
index ff4bda9a27..d97e4091a2 100644
--- a/var/spack/repos/builtin.mock/packages/openblas/package.py
+++ b/var/spack/repos/builtin.mock/packages/openblas/package.py
@@ -12,5 +12,10 @@ class Openblas(Package):
     url      = "http://github.com/xianyi/OpenBLAS/archive/v0.2.15.tar.gz"
 
     version('0.2.15', 'b1190f3d3471685f17cfd1ec1d252ac9')
+    version('0.2.14', 'b1190f3d3471685f17cfd1ec1d252ac9')
+    version('0.2.13', 'b1190f3d3471685f17cfd1ec1d252ac9')
+
+    # See #20019 for this conflict
+    conflicts('%gcc@:4.4.99', when='@0.2.14:')
 
     provides('blas')