diff --git a/Cargo.toml b/Cargo.toml
index a796249e..b9caae8f 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -22,6 +22,7 @@ include = ["Cargo.toml", "LICENSE", "README.md", "src/**", "tests/**", "examples
 [dependencies]
 thiserror = "1.0"
 rustc-hash = "1.1.0"
+indexmap = "1.6.2"
 serde = { version = "1.0", features = ["derive"], optional = true }
 log = "0.4.14" # for debug logs in tests
 
diff --git a/src/internal/partial_solution.rs b/src/internal/partial_solution.rs
index 23960a45..d85620e4 100644
--- a/src/internal/partial_solution.rs
+++ b/src/internal/partial_solution.rs
@@ -10,11 +10,15 @@ use crate::internal::incompatibility::{IncompId, Incompatibility, Relation};
 use crate::internal::small_map::SmallMap;
 use crate::package::Package;
 use crate::term::Term;
-use crate::type_aliases::{Map, SelectedDependencies};
+use crate::type_aliases::SelectedDependencies;
 use crate::version_set::VersionSet;
 
 use super::small_vec::SmallVec;
 
+use std::hash::BuildHasherDefault;
+
+type FnvIndexMap<K, V> = indexmap::IndexMap<K, V, BuildHasherDefault<rustc_hash::FxHasher>>;
+
 #[derive(Debug, Copy, Clone, Ord, PartialOrd, Eq, PartialEq)]
 pub struct DecisionLevel(pub u32);
 
@@ -30,7 +34,7 @@ impl DecisionLevel {
 pub struct PartialSolution<P: Package, VS: VersionSet> {
     next_global_index: u32,
     current_decision_level: DecisionLevel,
-    package_assignments: Map<P, PackageAssignments<P, VS>>,
+    package_assignments: FnvIndexMap<P, PackageAssignments<P, VS>>,
 }
 
 impl<P: Package, VS: VersionSet> Display for PartialSolution<P, VS> {
@@ -126,7 +130,7 @@ impl<P: Package, VS: VersionSet> PartialSolution<P, VS> {
         Self {
             next_global_index: 0,
             current_decision_level: DecisionLevel(0),
-            package_assignments: Map::default(),
+            package_assignments: FnvIndexMap::default(),
         }
     }
 
@@ -146,10 +150,11 @@ impl<P: Package, VS: VersionSet> PartialSolution<P, VS> {
                 },
             }
         }
+        let new_idx = self.current_decision_level.0 as usize;
         self.current_decision_level = self.current_decision_level.increment();
-        let mut pa = self
+        let (old_idx, _, mut pa) = self
             .package_assignments
-            .get_mut(&package)
+            .get_full_mut(&package)
             .expect("Derivations must already exist");
         pa.highest_decision_level = self.current_decision_level;
         pa.assignments_intersection = AssignmentsIntersection::Decision((
@@ -157,6 +162,9 @@ impl<P: Package, VS: VersionSet> PartialSolution<P, VS> {
             version.clone(),
             Term::exact(version),
         ));
+        if new_idx != old_idx {
+            self.package_assignments.swap_indices(new_idx, old_idx);
+        }
         self.next_global_index += 1;
     }
 
@@ -167,7 +175,7 @@ impl<P: Package, VS: VersionSet> PartialSolution<P, VS> {
         cause: IncompId<P, VS>,
         store: &Arena<Incompatibility<P, VS>>,
     ) {
-        use std::collections::hash_map::Entry;
+        use indexmap::map::Entry;
         let term = store[cause].get(&package).unwrap().negate();
         let dated_derivation = DatedDerivation {
             global_index: self.next_global_index,
@@ -208,9 +216,8 @@ impl<P: Package, VS: VersionSet> PartialSolution<P, VS> {
     /// and if it contains at least one positive derivation term
     /// in the partial solution.
     pub fn potential_packages(&self) -> Option<impl Iterator<Item = (&P, &VS)>> {
-        let mut iter = self
-            .package_assignments
-            .iter()
+        let mut iter = (self.current_decision_level.0 as usize..self.package_assignments.len())
+            .map(move |i| self.package_assignments.get_index(i).unwrap())
             .filter_map(|(p, pa)| pa.assignments_intersection.potential_package_filter(p))
             .peekable();
         if iter.peek().is_some() {
@@ -223,21 +230,17 @@ impl<P: Package, VS: VersionSet> PartialSolution<P, VS> {
     /// If a partial solution has, for every positive derivation,
     /// a corresponding decision that satisfies that assignment,
     /// it's a total solution and version solving has succeeded.
-    pub fn extract_solution(&self) -> Option<SelectedDependencies<P, VS::V>> {
-        let mut solution = Map::default();
-        for (p, pa) in &self.package_assignments {
-            match &pa.assignments_intersection {
-                AssignmentsIntersection::Decision((_, v, _)) => {
-                    solution.insert(p.clone(), v.clone());
-                }
-                AssignmentsIntersection::Derivations(term) => {
-                    if term.is_positive() {
-                        return None;
-                    }
+    pub fn extract_solution(&self) -> SelectedDependencies<P, VS::V> {
+        self.package_assignments
+            .iter()
+            .take(self.current_decision_level.0 as usize)
+            .map(|(p, pa)| match &pa.assignments_intersection {
+                AssignmentsIntersection::Decision((_, v, _)) => (p.clone(), v.clone()),
+                AssignmentsIntersection::Derivations(_) => {
+                    panic!("Derivations in the Decision part")
                 }
-            }
-        }
-        Some(solution)
+            })
+            .collect()
     }
 
     /// Backtrack the partial solution to a given decision level.
@@ -380,7 +383,7 @@ impl<P: Package, VS: VersionSet> PartialSolution<P, VS> {
     /// to return a coherent previous_satisfier_level.
     fn find_satisfier(
         incompat: &Incompatibility<P, VS>,
-        package_assignments: &Map<P, PackageAssignments<P, VS>>,
+        package_assignments: &FnvIndexMap<P, PackageAssignments<P, VS>>,
         store: &Arena<Incompatibility<P, VS>>,
     ) -> SmallMap<P, (usize, u32, DecisionLevel)> {
         let mut satisfied = SmallMap::Empty;
@@ -401,7 +404,7 @@ impl<P: Package, VS: VersionSet> PartialSolution<P, VS> {
         incompat: &Incompatibility<P, VS>,
         satisfier_package: &P,
         mut satisfied_map: SmallMap<P, (usize, u32, DecisionLevel)>,
-        package_assignments: &Map<P, PackageAssignments<P, VS>>,
+        package_assignments: &FnvIndexMap<P, PackageAssignments<P, VS>>,
         store: &Arena<Incompatibility<P, VS>>,
     ) -> DecisionLevel {
         // First, let's retrieve the previous derivations and the initial accum_term.
diff --git a/src/solver.rs b/src/solver.rs
index 846f220c..f2fc4eb5 100644
--- a/src/solver.rs
+++ b/src/solver.rs
@@ -107,11 +107,7 @@ pub fn resolve<P: Package, VS: VersionSet>(
             // The borrow checker did not like using a match on potential_packages.
             // This `if ... is_none ... drop` is a workaround.
             // I believe this is a case where Polonius could help, when and if it lands in rustc.
-            return state.partial_solution.extract_solution().ok_or_else(|| {
-                PubGrubError::Failure(
-                    "How did we end up with no package to choose but no solution?".into(),
-                )
-            });
+            return Ok(state.partial_solution.extract_solution());
         }
         let decision = dependency_provider
             .choose_package_version(potential_packages.unwrap())