diff --git a/compiler/rustc_data_structures/src/graph/dominators/mod.rs b/compiler/rustc_data_structures/src/graph/dominators/mod.rs
index 7cb013fdbd8..85b030c1a48 100644
--- a/compiler/rustc_data_structures/src/graph/dominators/mod.rs
+++ b/compiler/rustc_data_structures/src/graph/dominators/mod.rs
@@ -9,8 +9,6 @@
 //! Thomas Lengauer and Robert Endre Tarjan.
 //! <https://www.cs.princeton.edu/courses/archive/spr03/cs423/download/dominators.pdf>
 
-use std::cmp::Ordering;
-
 use rustc_index::{Idx, IndexSlice, IndexVec};
 
 use super::ControlFlowGraph;
@@ -64,9 +62,6 @@ fn is_small_path_graph<G: ControlFlowGraph>(g: &G) -> bool {
 }
 
 fn dominators_impl<G: ControlFlowGraph>(graph: &G) -> Inner<G::Node> {
-    // compute the post order index (rank) for each node
-    let mut post_order_rank = IndexVec::from_elem_n(0, graph.num_nodes());
-
     // We allocate capacity for the full set of nodes, because most of the time
     // most of the nodes *are* reachable.
     let mut parent: IndexVec<PreorderIndex, PreorderIndex> =
@@ -83,12 +78,10 @@ fn dominators_impl<G: ControlFlowGraph>(graph: &G) -> Inner<G::Node> {
     pre_order_to_real.push(graph.start_node());
     parent.push(PreorderIndex::ZERO); // the parent of the root node is the root for now.
     real_to_pre_order[graph.start_node()] = Some(PreorderIndex::ZERO);
-    let mut post_order_idx = 0;
 
     // Traverse the graph, collecting a number of things:
     //
     // * Preorder mapping (to it, and back to the actual ordering)
-    // * Postorder mapping (used exclusively for `cmp_in_dominator_order` on the final product)
     // * Parents for each vertex in the preorder tree
     //
     // These are all done here rather than through one of the 'standard'
@@ -104,8 +97,6 @@ fn dominators_impl<G: ControlFlowGraph>(graph: &G) -> Inner<G::Node> {
                 continue 'recurse;
             }
         }
-        post_order_rank[pre_order_to_real[frame.pre_order_idx]] = post_order_idx;
-        post_order_idx += 1;
 
         stack.pop();
     }
@@ -282,7 +273,7 @@ fn dominators_impl<G: ControlFlowGraph>(graph: &G) -> Inner<G::Node> {
 
     let time = compute_access_time(start_node, &immediate_dominators);
 
-    Inner { post_order_rank, immediate_dominators, time }
+    Inner { immediate_dominators, time }
 }
 
 /// Evaluate the link-eval virtual forest, providing the currently minimum semi
@@ -348,7 +339,6 @@ fn compress(
 /// Tracks the list of dominators for each node.
 #[derive(Clone, Debug)]
 struct Inner<N: Idx> {
-    post_order_rank: IndexVec<N, usize>,
     // Even though we track only the immediate dominator of each node, it's
     // possible to get its full list of dominators by looking up the dominator
     // of each dominator.
@@ -379,17 +369,6 @@ impl<Node: Idx> Dominators<Node> {
         }
     }
 
-    /// Provide deterministic ordering of nodes such that, if any two nodes have a dominator
-    /// relationship, the dominator will always precede the dominated. (The relative ordering
-    /// of two unrelated nodes will also be consistent, but otherwise the order has no
-    /// meaning.) This method cannot be used to determine if either Node dominates the other.
-    pub fn cmp_in_dominator_order(&self, lhs: Node, rhs: Node) -> Ordering {
-        match &self.kind {
-            Kind::Path => lhs.index().cmp(&rhs.index()),
-            Kind::General(g) => g.post_order_rank[rhs].cmp(&g.post_order_rank[lhs]),
-        }
-    }
-
     /// Returns true if `a` dominates `b`.
     ///
     /// # Panics
diff --git a/compiler/rustc_mir_transform/src/coverage/graph.rs b/compiler/rustc_mir_transform/src/coverage/graph.rs
index d839f46cfbd..930fa129ef2 100644
--- a/compiler/rustc_mir_transform/src/coverage/graph.rs
+++ b/compiler/rustc_mir_transform/src/coverage/graph.rs
@@ -21,6 +21,10 @@ pub(crate) struct CoverageGraph {
     pub(crate) successors: IndexVec<BasicCoverageBlock, Vec<BasicCoverageBlock>>,
     pub(crate) predecessors: IndexVec<BasicCoverageBlock, Vec<BasicCoverageBlock>>,
     dominators: Option<Dominators<BasicCoverageBlock>>,
+    /// Allows nodes to be compared in some total order such that _if_
+    /// `a` dominates `b`, then `a < b`. If neither node dominates the other,
+    /// their relative order is consistent but arbitrary.
+    dominator_order_rank: IndexVec<BasicCoverageBlock, u32>,
 }
 
 impl CoverageGraph {
@@ -54,10 +58,27 @@ impl CoverageGraph {
             }
         }
 
-        let mut this = Self { bcbs, bb_to_bcb, successors, predecessors, dominators: None };
+        let num_nodes = bcbs.len();
+        let mut this = Self {
+            bcbs,
+            bb_to_bcb,
+            successors,
+            predecessors,
+            dominators: None,
+            dominator_order_rank: IndexVec::from_elem_n(0, num_nodes),
+        };
+        assert_eq!(num_nodes, this.num_nodes());
 
         this.dominators = Some(dominators::dominators(&this));
 
+        // The dominator rank of each node is just its index in a reverse-postorder traversal.
+        let reverse_post_order = graph::iterate::reverse_post_order(&this, this.start_node());
+        // The coverage graph is created by traversal, so all nodes are reachable.
+        assert_eq!(reverse_post_order.len(), this.num_nodes());
+        for (rank, bcb) in (0u32..).zip(reverse_post_order) {
+            this.dominator_order_rank[bcb] = rank;
+        }
+
         // The coverage graph's entry-point node (bcb0) always starts with bb0,
         // which never has predecessors. Any other blocks merged into bcb0 can't
         // have multiple (coverage-relevant) predecessors, so bcb0 always has
@@ -162,7 +183,7 @@ impl CoverageGraph {
         a: BasicCoverageBlock,
         b: BasicCoverageBlock,
     ) -> Ordering {
-        self.dominators.as_ref().unwrap().cmp_in_dominator_order(a, b)
+        self.dominator_order_rank[a].cmp(&self.dominator_order_rank[b])
     }
 
     /// Returns the source of this node's sole in-edge, if it has exactly one.