diff --git a/compiler/can/src/module.rs b/compiler/can/src/module.rs
index 50053a823a..fad4785f56 100644
--- a/compiler/can/src/module.rs
+++ b/compiler/can/src/module.rs
@@ -26,13 +26,19 @@ pub struct Module {
     pub referenced_values: MutSet<Symbol>,
     pub referenced_types: MutSet<Symbol>,
     pub aliases: MutMap<Symbol, Alias>,
-    pub rigid_variables: MutMap<Variable, Lowercase>,
+    pub rigid_variables: RigidVariables,
+}
+
+#[derive(Debug, Default)]
+pub struct RigidVariables {
+    pub named: MutMap<Variable, Lowercase>,
+    pub wildcards: MutSet<Variable>,
 }
 
 #[derive(Debug)]
 pub struct ModuleOutput {
     pub aliases: MutMap<Symbol, Alias>,
-    pub rigid_variables: MutMap<Variable, Lowercase>,
+    pub rigid_variables: RigidVariables,
     pub declarations: Vec<Declaration>,
     pub exposed_imports: MutMap<Symbol, Variable>,
     pub lookups: Vec<(Symbol, Variable, Region)>,
@@ -169,7 +175,7 @@ pub fn canonicalize_module_defs<'a>(
     }
 
     let mut lookups = Vec::with_capacity(num_deps);
-    let mut rigid_variables = MutMap::default();
+    let mut rigid_variables = RigidVariables::default();
 
     // Exposed values are treated like defs that appear before any others, e.g.
     //
@@ -249,11 +255,11 @@ pub fn canonicalize_module_defs<'a>(
     }
 
     for (var, lowercase) in output.introduced_variables.name_by_var {
-        rigid_variables.insert(var, lowercase.clone());
+        rigid_variables.named.insert(var, lowercase.clone());
     }
 
     for var in output.introduced_variables.wildcards {
-        rigid_variables.insert(var, "*".into());
+        rigid_variables.wildcards.insert(var);
     }
 
     let mut referenced_values = MutSet::default();
diff --git a/compiler/solve/src/module.rs b/compiler/solve/src/module.rs
index abd3b32a70..6508302d96 100644
--- a/compiler/solve/src/module.rs
+++ b/compiler/solve/src/module.rs
@@ -1,7 +1,7 @@
 use crate::solve;
 use roc_can::constraint::{Constraint as ConstraintSoa, Constraints};
+use roc_can::module::RigidVariables;
 use roc_collections::all::MutMap;
-use roc_module::ident::Lowercase;
 use roc_module::symbol::Symbol;
 use roc_types::solved_types::{Solved, SolvedType};
 use roc_types::subs::{StorageSubs, Subs, Variable};
@@ -29,15 +29,19 @@ pub struct SolvedModule {
 pub fn run_solve(
     constraints: &Constraints,
     constraint: ConstraintSoa,
-    rigid_variables: MutMap<Variable, Lowercase>,
+    rigid_variables: RigidVariables,
     mut subs: Subs,
 ) -> (Solved<Subs>, solve::Env, Vec<solve::TypeError>) {
     let env = solve::Env::default();
 
-    for (var, name) in rigid_variables {
+    for (var, name) in rigid_variables.named {
         subs.rigid_var(var, name);
     }
 
+    for var in rigid_variables.wildcards {
+        subs.rigid_var(var, "*".into());
+    }
+
     // Now that the module is parsed, canonicalized, and constrained,
     // we need to type check it.
     let mut problems = Vec::new();