diff --git a/lib/spack/spack/solver/asp.py b/lib/spack/spack/solver/asp.py
index c6db80e878b..bd1527c09a2 100644
--- a/lib/spack/spack/solver/asp.py
+++ b/lib/spack/spack/solver/asp.py
@@ -159,7 +159,7 @@ def getter(node):
 
 
 def build_criteria_names(
-    costs: List[int], opt_criteria: List["AspFunction"], max_depth: int, const_max_depth: int
+    costs: List[int], opt_criteria: List["AspFunction"], max_depth: int
 ) -> Dict[str, Union[int, List[Tuple[int, int]]]]:
     """Construct an ordered mapping from criteria names to costs."""
 
@@ -174,8 +174,12 @@ def build_criteria_names(
     # first non-error criterion
     solve_index = max_error_priority + 1
 
-    # each criterion is aggregated for each level in the graph
-    max_leveled_costs = len(leveled_criteria) * const_max_depth
+    # compute without needing max_depth from solve
+    max_leveled_costs = (len(costs) - max_error_priority - 3) / 2
+    assert max_leveled_costs * 2 == len(costs) - max_error_priority - 3
+    assert max_leveled_costs % len(leveled_criteria) == 0
+    max_leveled_costs = int(max_leveled_costs)
+
     n_leveled_costs = len(leveled_criteria) * (max_depth + 1)
 
     build_index = solve_index + 1 + max_leveled_costs
@@ -794,11 +798,11 @@ def on_model(model):
             # get optimization criteria
             criteria = extract_functions(best_model, "opt_criterion")
             depths = extract_functions(best_model, "depth")
-            const_max_depth, *_ = extract_functions(best_model, "const_max_depth")
-            const_max_depth = const_max_depth.args[0]
             max_depth = max(d.args[1] for d in depths)
 
-            result.criteria = build_criteria_names(min_cost, criteria, max_depth, const_max_depth)
+            print("PRIO:", priorities)
+
+            result.criteria = build_criteria_names(min_cost, criteria, max_depth)
 
             # record the number of models the solver considered
             result.nmodels = len(models)
diff --git a/lib/spack/spack/solver/concretize.lp b/lib/spack/spack/solver/concretize.lp
index ac1c94ab337..9c640a3745a 100644
--- a/lib/spack/spack/solver/concretize.lp
+++ b/lib/spack/spack/solver/concretize.lp
@@ -1117,32 +1117,32 @@ build_priority(Package, build_prio) :- attr("node", Package), not optimize_for_r
 % Calculate min depth of nodes in the DAG
 % We use this to optimize nodes closer to roots with higher precedence.
 %-----------------------------------------------------------------------------
-#const max_depth = 5.
-const_max_depth(max_depth).
+#const max_depth = 10.
 
 % roots have depth 0.
 depth(Package, 0) :- attr("root", Package).
+depth(Package, D+1) :- depth(Dependent, D), depends_on(Dependent, Package), D < max_depth.
+
+
+%parent_depth(Package, D) :-
+%    depends_on(Dependent, Package),
+%    depth(Dependent, D),
+%    D < max_depth - 1.
+
+%depth(Package, M+1) :-
+%    M = #min{ D: parent_depth(Package, D); max_depth - 1 },
+%    attr("node", Package).
 
 % other nodes' depth is the minimum depth of any dependent plus one.
-min_parent_depth(Package, N) :-
-    N = #min{
-        D: depends_on(Dependent, Package),
-           depth(Dependent, D),
-           D = 0..max_depth - 1
-    },
-    N = 0..max_depth - 1,
-    attr("node", Package).
-
-depth(Package, max_depth - 1) :-
-    min_parent_depth(Package, P),
-    P >= max_depth - 1,
-    attr("node", Package).
-
-depth(Package, P+1) :-
-    min_parent_depth(Package, P),
-    P >= 0,
-    P < max_depth - 1,
-    attr("node", Package).
+%depth(Package, N + 1) :-
+%    N = #min{
+%        D: depends_on(Dependent, Package),
+%           depth(Dependent, D),
+%           D < max_depth;
+%        max_depth - 1
+%    },
+%    N = 0..max_depth - 1,
+%    attr("node", Package).
 
 
 %-----------------------------------------------------------------
@@ -1183,11 +1183,11 @@ depth(Package, P+1) :-
 % "leveled" criteria sum into a bucket per depth in the graph, per build priority
 #minimize{
     0@(((max_depth - D - 1) * depth_offset) + N + build_prio)
-    : opt_criterion(N, "leveled", _), D = 0..max_depth - 1
+    : opt_criterion(N, "leveled", _), depth(_, D)
 }.
 #minimize{
     0@(((max_depth - D - 1) * depth_offset) + N)
-    : opt_criterion(N, "leveled", _), D = 0..max_depth - 1
+    : opt_criterion(N, "leveled", _), depth(_, D)
 }.
 
 % Try hard to reuse installed packages (i.e., minimize the number built)
diff --git a/lib/spack/spack/solver/display.lp b/lib/spack/spack/solver/display.lp
index 7764c214f76..5c14c8f7a13 100644
--- a/lib/spack/spack/solver/display.lp
+++ b/lib/spack/spack/solver/display.lp
@@ -27,7 +27,7 @@
 
 % depths
 #show depth/2.
-#show const_max_depth/1.
+%#show parent_depth/2.
 
 % debug