diff --git a/lib/spack/spack/solver/asp.py b/lib/spack/spack/solver/asp.py
index e566b2fa944..8175b3ac0c8 100644
--- a/lib/spack/spack/solver/asp.py
+++ b/lib/spack/spack/solver/asp.py
@@ -159,10 +159,6 @@ def build_criteria_names(
     costs: List[int], opt_criteria: List["AspFunction"], max_depth: int
 ) -> Dict[str, Union[int, List[int]]]:
     """Construct an ordered mapping from criteria names to costs."""
-    print(costs)
-    print(len(costs))
-    print(max_depth)
-    print(opt_criteria)
 
     # ensure names of all criteria are unique
     names = {criterion.args[0] for criterion in opt_criteria}
@@ -776,7 +772,7 @@ def visit(node):
         cores = []  # unsatisfiable cores if they do not
 
         def on_model(model):
-            models.append((model.cost, model.symbols(shown=True, terms=True)))
+            models.append((model.cost, model.priority, model.symbols(shown=True, terms=True)))
 
         solve_kwargs = {
             "assumptions": self.assumptions,
@@ -797,7 +793,7 @@ def on_model(model):
         if result.satisfiable:
             # get the best model
             builder = SpecBuilder(specs, hash_lookup=setup.reusable_and_possible)
-            min_cost, best_model = min(models)
+            min_cost, priorities, best_model = min(models)
 
             # first check for errors
             error_args = [fn.args for fn in extract_functions(best_model, "error")]
@@ -818,6 +814,13 @@ def on_model(model):
             depths = extract_functions(best_model, "depth")
             print(depths)
             max_depth = max(d.args[1] for d in depths)
+
+            print(f"COST:      {len(min_cost)} {min_cost}")
+            print(f"PRIO:      {len(priorities)} {priorities}")
+            print(f"MAX_DEPTH: {max_depth}")
+            print()
+            print(opt_criteria)
+
             result.criteria = build_criteria_names(min_cost, criteria, max_depth)
 
             # record the number of models the solver considered
diff --git a/lib/spack/spack/solver/concretize.lp b/lib/spack/spack/solver/concretize.lp
index 1c8525cdf0c..00d4d4e37ec 100644
--- a/lib/spack/spack/solver/concretize.lp
+++ b/lib/spack/spack/solver/concretize.lp
@@ -1118,7 +1118,7 @@ build_priority(Package, 0)   :- attr("node", Package), not optimize_for_reuse().
 depth(Package, 0) :- attr("root", Package).
 
 % other nodes' depth is the minimum depth of any dependent plus one.
-depth(Package, N+1) :-
+min_parent_depth(Package, N) :-
     N = #min{
         D: depends_on(Dependent, Package),
            depth(Dependent, D),
@@ -1126,9 +1126,21 @@ depth(Package, N+1) :-
            D < max_depth
     },
     0 <= N,
-    N <= max_depth,
+    N < max_depth,
     attr("node", Package).
 
+depth(Package, max_depth) :-
+    min_parent_depth(Package, P),
+    P >= max_depth,
+    attr("node", Package).
+
+depth(Package, P+1) :-
+    min_parent_depth(Package, P),
+    P >= 0,
+    P < max_depth,
+    attr("node", Package).
+
+
 %-----------------------------------------------------------------
 % Optimization to avoid errors
 %-----------------------------------------------------------------
diff --git a/var/spack/repos/builtin/packages/clingo/package.py b/var/spack/repos/builtin/packages/clingo/package.py
index 70654c546f1..6502106e607 100644
--- a/var/spack/repos/builtin/packages/clingo/package.py
+++ b/var/spack/repos/builtin/packages/clingo/package.py
@@ -23,6 +23,8 @@ class Clingo(CMakePackage):
     url = "https://github.com/potassco/clingo/archive/v5.2.2.tar.gz"
     git = "https://github.com/potassco/clingo.git"
     tags = ["windows"]
+    submodules = True
+
     maintainers = ["tgamblin", "alalazo"]
 
     version("master", branch="master", submodules=True)