diff --git a/crates/compiler/load_internal/src/file.rs b/crates/compiler/load_internal/src/file.rs
index ae18e61db2..8758b0a3cc 100644
--- a/crates/compiler/load_internal/src/file.rs
+++ b/crates/compiler/load_internal/src/file.rs
@@ -4409,7 +4409,7 @@ pub fn add_imports(
 #[allow(clippy::complexity)]
 fn run_solve_solve(
     exposed_for_module: ExposedForModule,
-    types: Types,
+    mut types: Types,
     mut constraints: Constraints,
     constraint: ConstraintSoa,
     pending_derives: PendingDerives,
@@ -4451,7 +4451,7 @@ fn run_solve_solve(
 
     let mut solve_aliases = roc_solve::solve::Aliases::with_capacity(aliases.len());
     for (name, (_, alias)) in aliases.iter() {
-        solve_aliases.insert(*name, alias.clone());
+        solve_aliases.insert(&mut types, *name, alias.clone());
     }
 
     let (solved_subs, solved_implementations, exposed_vars_by_symbol, problems, abilities_store) = {
diff --git a/crates/compiler/solve/src/solve.rs b/crates/compiler/solve/src/solve.rs
index 70f94bddbf..a1ad9c51fc 100644
--- a/crates/compiler/solve/src/solve.rs
+++ b/crates/compiler/solve/src/solve.rs
@@ -138,7 +138,7 @@ impl DelayedAliasVariables {
 
 #[derive(Debug, Default)]
 pub struct Aliases {
-    aliases: Vec<(Symbol, Type, DelayedAliasVariables, AliasKind)>,
+    aliases: Vec<(Symbol, Index<TypeTag>, DelayedAliasVariables, AliasKind)>,
     variables: Vec<OptAbleVar>,
 }
 
@@ -150,7 +150,7 @@ impl Aliases {
         }
     }
 
-    pub fn insert(&mut self, symbol: Symbol, alias: Alias) {
+    pub fn insert(&mut self, types: &mut Types, symbol: Symbol, alias: Alias) {
         let alias_variables =
             {
                 let start = self.variables.len() as _;
@@ -195,8 +195,11 @@ impl Aliases {
                 }
             };
 
+        // TODO: can we construct Aliases from TypeTag directly?
+        let alias_typ = types.from_old_type(&alias.typ);
+
         self.aliases
-            .push((symbol, alias.typ, alias_variables, alias.kind));
+            .push((symbol, alias_typ, alias_variables, alias.kind));
     }
 
     fn instantiate_result_result(
@@ -335,19 +338,16 @@ impl Aliases {
             return (var, kind);
         }
 
-        let (typ, delayed_variables, &mut kind) =
-            match self.aliases.iter_mut().find(|(s, _, _, _)| *s == symbol) {
+        let (typ, delayed_variables, kind) =
+            match self.aliases.iter().find(|(s, _, _, _)| *s == symbol) {
                 None => internal_error!(
                     "Alias {:?} not registered in delayed aliases! {:?}",
                     symbol,
                     &self.aliases
                 ),
-                Some((_, typ, delayed_variables, kind)) => (typ, delayed_variables, kind),
+                Some(&(_, typ, delayed_variables, kind)) => (typ, delayed_variables, kind),
             };
 
-        // TODO(types-soa) store SoA type in aliases directly
-        let typ = types.from_old_type(typ);
-
         let mut substitutions: MutMap<_, _> = Default::default();
 
         let old_type_variables = delayed_variables.type_variables(&mut self.variables);
diff --git a/crates/reporting/tests/helpers/mod.rs b/crates/reporting/tests/helpers/mod.rs
index 8afb2f7303..195a27b6b3 100644
--- a/crates/reporting/tests/helpers/mod.rs
+++ b/crates/reporting/tests/helpers/mod.rs
@@ -18,7 +18,7 @@ use roc_region::all::Loc;
 use roc_solve::solve::{self, Aliases};
 use roc_solve_problem::TypeError;
 use roc_types::subs::{Content, Subs, VarStore, Variable};
-use roc_types::types::Type;
+use roc_types::types::{Type, Types};
 use std::hash::Hash;
 use std::path::{Path, PathBuf};
 
@@ -31,6 +31,7 @@ pub fn test_home() -> ModuleId {
 pub fn infer_expr(
     subs: Subs,
     problems: &mut Vec<TypeError>,
+    types: Types,
     constraints: &Constraints,
     constraint: &Constraint,
     pending_derives: PendingDerives,
@@ -41,7 +42,7 @@ pub fn infer_expr(
 ) -> (Content, Subs) {
     let (solved, _) = solve::run(
         ModuleId::ATTR,
-        Default::default(),
+        types,
         constraints,
         problems,
         subs,
@@ -113,6 +114,7 @@ pub struct CanExprOut {
     pub var: Variable,
     pub constraint: Constraint,
     pub constraints: Constraints,
+    pub types: Types,
 }
 
 #[derive(Debug)]
@@ -203,6 +205,7 @@ pub fn can_expr_with<'a>(
         var,
         constraint,
         constraints,
+        types: Default::default(),
     })
 }
 
diff --git a/crates/reporting/tests/test_reporting.rs b/crates/reporting/tests/test_reporting.rs
index 306df586c8..4288582dd0 100644
--- a/crates/reporting/tests/test_reporting.rs
+++ b/crates/reporting/tests/test_reporting.rs
@@ -202,6 +202,7 @@ mod test_reporting {
             home,
             interns,
             problems: can_problems,
+            mut types,
             ..
         } = can_expr(arena, expr_src)?;
         let mut subs = Subs::new_from_varstore(var_store);
@@ -217,7 +218,7 @@ mod test_reporting {
         let mut solve_aliases = roc_solve::solve::Aliases::default();
 
         for (name, alias) in output.aliases {
-            solve_aliases.insert(name, alias);
+            solve_aliases.insert(&mut types, name, alias);
         }
 
         let mut unify_problems = Vec::new();
@@ -225,6 +226,7 @@ mod test_reporting {
         let (_content, _subs) = infer_expr(
             subs,
             &mut unify_problems,
+            types,
             &constraints,
             &constraint,
             // Use `new_report_problem_as` in order to get proper derives.