diff --git a/src/group/stabchain/base_change_builder/random.rs b/src/group/stabchain/base_change_builder/random.rs
index 6d1623a2a1..6853b91742 100644
--- a/src/group/stabchain/base_change_builder/random.rs
+++ b/src/group/stabchain/base_change_builder/random.rs
@@ -3,17 +3,12 @@ use crate::DetHashSet;
 use crate::{
     group::{
         orbit::abstraction::{FactoredTransversalResolver, TransversalResolver},
-        random_perm::RandPerm,
         stabchain::{base::Base, Stabchain, StabchainRecord},
-        Group,
     },
     perm::{actions::SimpleApplication, Action, Permutation},
 };
 use num::BigUint;
 
-const MIN_SIZE: usize = 11;
-const INITIAL_RUNS: usize = 50;
-
 /// Helper struct, used to build the stabilizer chain
 pub struct RandomBaseChangeBuilder<P, A = SimpleApplication<P>>
 where
@@ -40,7 +35,6 @@ where
         V: TransversalResolver<P, A>,
     {
         let target_order = chain.order();
-        let sgs = Group::from_list(chain.strong_generating_set());
         // Create the trivial chain with all the new base points.
         self.chain = base
             .base()
@@ -48,11 +42,10 @@ where
             .cloned()
             .map(StabchainRecord::trivial_record)
             .collect::<Vec<_>>();
-        //Random permutation generator.
-        let mut rand_perm = RandPerm::new(MIN_SIZE, &sgs, INITIAL_RUNS, rand::thread_rng());
+        let mut rng = rand::thread_rng();
         //Loop till the new chain has the correct order.
         while self.current_chain_order() < target_order {
-            let g = rand_perm.random_permutation();
+            let g = chain.random_element(&mut rng);
             let (g_dash, i) = self.residue_with_dropout(g);
             //If the permutation doesn't sift through then add it as a new generator at level i.
             if i < base.base().len() {
diff --git a/src/group/stabchain/mod.rs b/src/group/stabchain/mod.rs
index a56d392a24..bd71c3ccce 100644
--- a/src/group/stabchain/mod.rs
+++ b/src/group/stabchain/mod.rs
@@ -12,6 +12,7 @@ use crate::perm::*;
 use base::Base;
 use base_change_builder::{BaseChangeBuilder, BaseChangeBuilderStrategy};
 use builder::{Builder, BuilderStrategy};
+use rand::seq::IteratorRandom;
 
 use crate::DetHashMap;
 
@@ -145,6 +146,47 @@ where
         builder.set_base(self, base);
         builder.build()
     }
+
+    /// Get a random element of the group at a specific layer of the chain.
+    /// This will generate elements uniformly, assuming the given RNG also does.
+    pub fn random_element_from_layer<R>(&self, layer: usize, rng: &mut R) -> P
+    where
+        R: rand::Rng,
+    {
+        self.get_chain_at_layer(layer)
+            .map(|record| {
+                record
+                    .resolver()
+                    .representative(
+                        &record.transversal,
+                        record.base.clone(),
+                        record
+                            .transversal
+                            .keys()
+                            .choose(rng)
+                            .unwrap_or(&record.base)
+                            .clone(),
+                    )
+                    .unwrap()
+            })
+            .fold(P::id(), |accum, product| accum.multiply(&product))
+    }
+
+    /// Get a random element of the group this chain represents.
+    /// This will generate elements uniformly, assuming the given RNG also does.
+    /// ```
+    /// use stabchain::group::Group;
+    /// let g = Group::symmetric(4);
+    /// let chain = g.stabchain();
+    /// let p = chain.random_element(&mut rand::thread_rng());
+    /// assert!(chain.in_group(&p));
+    ///```
+    pub fn random_element<R>(&self, rng: &mut R) -> P
+    where
+        R: rand::Rng,
+    {
+        self.random_element_from_layer(0, rng)
+    }
 }
 
 impl<P, A> Stabchain<P, FactoredTransversalResolver<A>, A>