diff --git a/app-proto/Cargo.lock b/app-proto/Cargo.lock
index 9738589..e6cb21a 100644
--- a/app-proto/Cargo.lock
+++ b/app-proto/Cargo.lock
@@ -1,6 +1,6 @@
 # This file is automatically @generated by Cargo.
 # It is not intended for manual editing.
-version = 3
+version = 4
 
 [[package]]
 name = "ahash"
@@ -90,7 +90,6 @@ dependencies = [
  "nalgebra",
  "readonly",
  "rustc-hash",
- "slab",
  "sycamore",
  "wasm-bindgen-test",
  "web-sys",
@@ -414,15 +413,6 @@ dependencies = [
  "wide",
 ]
 
-[[package]]
-name = "slab"
-version = "0.4.9"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "8f92a496fb766b417c996b9c5e57daf2f7ad3b0bebe1ccfca4856390e3d3bb67"
-dependencies = [
- "autocfg",
-]
-
 [[package]]
 name = "slotmap"
 version = "1.0.7"
diff --git a/app-proto/Cargo.toml b/app-proto/Cargo.toml
index 77952f9..662e123 100644
--- a/app-proto/Cargo.toml
+++ b/app-proto/Cargo.toml
@@ -16,7 +16,6 @@ lazy_static = "1.5.0"
 nalgebra = "0.33.0"
 readonly = "0.2.12"
 rustc-hash = "2.0.0"
-slab = "0.4.9"
 sycamore = "0.9.0-beta.3"
 
 # The `console_error_panic_hook` crate provides better debugging of panics by
diff --git a/app-proto/src/assembly.rs b/app-proto/src/assembly.rs
index a20993b..ab43a8c 100644
--- a/app-proto/src/assembly.rs
+++ b/app-proto/src/assembly.rs
@@ -1,14 +1,15 @@
 use nalgebra::{DMatrix, DVector, DVectorView};
 use rustc_hash::FxHashMap;
-use slab::Slab;
 use std::{
     any::{Any, TypeId},
     cell::Cell,
+    collections::BTreeSet,
+    cmp::Ordering,
     fmt,
     fmt::{Debug, Formatter},
     hash::{Hash, Hasher},
     rc::Rc,
-    sync::atomic::{AtomicU64, Ordering}
+    sync::{atomic, atomic::AtomicU64}
 };
 use sycamore::prelude::*;
 use web_sys::{console, wasm_bindgen::JsValue}; /* DEBUG */
@@ -29,9 +30,6 @@ use crate::{
     specified::SpecifiedValue
 };
 
-// the types of the keys we use to access an assembly's elements
-pub type ElementKey = usize;
-
 pub type ElementColor = [f32; 3];
 
 /* KLUDGE */
@@ -53,7 +51,7 @@ pub trait Serial {
         //   https://marabos.nl/atomics/atomics.html#example-handle-overflow
         //
         NEXT_SERIAL.fetch_update(
-            Ordering::SeqCst, Ordering::SeqCst,
+            atomic::Ordering::SeqCst, atomic::Ordering::SeqCst,
             |serial| serial.checked_add(1)
         ).expect("Out of serial numbers for elements")
     }
@@ -73,6 +71,18 @@ impl PartialEq for dyn Serial {
 
 impl Eq for dyn Serial {}
 
+impl PartialOrd for dyn Serial {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        Some(self.cmp(other))
+    }
+}
+
+impl Ord for dyn Serial {
+    fn cmp(&self, other: &Self) -> Ordering {
+        self.serial().cmp(&other.serial())
+    }
+}
+
 pub trait ProblemPoser {
     fn pose(&self, problem: &mut ConstraintProblem);
 }
@@ -95,7 +105,7 @@ pub trait Element: Serial + ProblemPoser + DisplayItem {
     
     // the regulators the element is subject to. the assembly that owns the
     // element is responsible for keeping this set up to date
-    fn regulators(&self) -> Signal<Vec<Rc<dyn Regulator>>>;
+    fn regulators(&self) -> Signal<BTreeSet<Rc<dyn Regulator>>>;
     
     // the configuration matrix column index that was assigned to the element
     // last time the assembly was realized, or `None` if the element has never
@@ -128,12 +138,24 @@ impl PartialEq for dyn Element {
 
 impl Eq for dyn Element {}
 
+impl PartialOrd for dyn Element {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        <dyn Serial>::partial_cmp(self, other)
+    }
+}
+
+impl Ord for dyn Element {
+    fn cmp(&self, other: &Self) -> Ordering {
+        <dyn Serial>::cmp(self, other)
+    }
+}
+
 pub struct Sphere {
     pub id: String,
     pub label: String,
     pub color: ElementColor,
     pub representation: Signal<DVector<f64>>,
-    pub regulators: Signal<Vec<Rc<dyn Regulator>>>,
+    pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
     serial: u64,
     column_index: Cell<Option<usize>>
 }
@@ -152,7 +174,7 @@ impl Sphere {
             label: label,
             color: color,
             representation: create_signal(representation),
-            regulators: create_signal(Vec::new()),
+            regulators: create_signal(BTreeSet::new()),
             serial: Self::next_serial(),
             column_index: None.into()
         }
@@ -189,7 +211,7 @@ impl Element for Sphere {
         self.representation
     }
     
-    fn regulators(&self) -> Signal<Vec<Rc<dyn Regulator>>> {
+    fn regulators(&self) -> Signal<BTreeSet<Rc<dyn Regulator>>> {
         self.regulators
     }
     
@@ -223,7 +245,7 @@ pub struct Point {
     pub label: String,
     pub color: ElementColor,
     pub representation: Signal<DVector<f64>>,
-    pub regulators: Signal<Vec<Rc<dyn Regulator>>>,
+    pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
     serial: u64,
     column_index: Cell<Option<usize>>
 }
@@ -242,7 +264,7 @@ impl Point {
             label,
             color,
             representation: create_signal(representation),
-            regulators: create_signal(Vec::new()),
+            regulators: create_signal(BTreeSet::new()),
             serial: Self::next_serial(),
             column_index: None.into()
         }
@@ -275,7 +297,7 @@ impl Element for Point {
         self.representation
     }
     
-    fn regulators(&self) -> Signal<Vec<Rc<dyn Regulator>>> {
+    fn regulators(&self) -> Signal<BTreeSet<Rc<dyn Regulator>>> {
         self.regulators
     }
     
@@ -335,6 +357,18 @@ impl PartialEq for dyn Regulator {
 
 impl Eq for dyn Regulator {}
 
+impl PartialOrd for dyn Regulator {
+    fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
+        <dyn Serial>::partial_cmp(self, other)
+    }
+}
+
+impl Ord for dyn Regulator {
+    fn cmp(&self, other: &Self) -> Ordering {
+        <dyn Serial>::cmp(self, other)
+    }
+}
+
 pub struct InversiveDistanceRegulator {
     pub subjects: [Rc<dyn Element>; 2],
     pub measurement: ReadSignal<f64>,
@@ -472,8 +506,8 @@ type AssemblyMotion<'a> = Vec<ElementMotion<'a>>;
 #[derive(Clone)]
 pub struct Assembly {
     // elements and regulators
-    pub elements: Signal<Slab<Rc<dyn Element>>>,
-    pub regulators: Signal<Slab<Rc<dyn Regulator>>>,
+    pub elements: Signal<BTreeSet<Rc<dyn Element>>>,
+    pub regulators: Signal<BTreeSet<Rc<dyn Regulator>>>,
     
     // solution variety tangent space. the basis vectors are stored in
     // configuration matrix format, ordered according to the elements' column
@@ -494,8 +528,8 @@ pub struct Assembly {
 impl Assembly {
     pub fn new() -> Assembly {
         Assembly {
-            elements: create_signal(Slab::new()),
-            regulators: create_signal(Slab::new()),
+            elements: create_signal(BTreeSet::new()),
+            regulators: create_signal(BTreeSet::new()),
             tangent: create_signal(ConfigSubspace::zero(0)),
             elements_by_id: create_signal(FxHashMap::default())
         }
@@ -506,30 +540,27 @@ impl Assembly {
     // insert an element into the assembly without checking whether we already
     // have an element with the same identifier. any element that does have the
     // same identifier will get kicked out of the `elements_by_id` index
-    fn insert_element_unchecked(&self, elt: impl Element + 'static) -> ElementKey {
+    fn insert_element_unchecked(&self, elt: impl Element + 'static) {
         // insert the element
         let id = elt.id().clone();
         let elt_rc = Rc::new(elt);
-        let key = self.elements.update(|elts| elts.insert(elt_rc.clone()));
+        self.elements.update(|elts| elts.insert(elt_rc.clone()));
         self.elements_by_id.update(|elts_by_id| elts_by_id.insert(id, elt_rc.clone()));
         
         // create and insert the element's default regulators
         for reg in elt_rc.default_regulators() {
             self.insert_regulator(reg);
         }
-        
-        key
     }
     
-    pub fn try_insert_element(&self, elt: impl Element + 'static) -> Option<ElementKey> {
+    pub fn try_insert_element(&self, elt: impl Element + 'static) -> bool {
         let can_insert = self.elements_by_id.with_untracked(
             |elts_by_id| !elts_by_id.contains_key(elt.id())
         );
         if can_insert {
-            Some(self.insert_element_unchecked(elt))
-        } else {
-            None
+            self.insert_element_unchecked(elt);
         }
+        can_insert
     }
     
     pub fn insert_element_default<T: Element + 'static>(&self) {
@@ -559,7 +590,7 @@ impl Assembly {
             |subj| subj.regulators()
         ).collect();
         for regulators in subject_regulators {
-            regulators.update(|regs| regs.push(regulator.clone()));
+            regulators.update(|regs| regs.insert(regulator.clone()));
         }
         
         // update the realization when the regulator becomes a constraint, or is
@@ -581,7 +612,7 @@ impl Assembly {
         // print an updated list of regulators
         console::log_1(&JsValue::from("Regulators:"));
         self.regulators.with_untracked(|regs| {
-            for (_, reg) in regs.into_iter() {
+            for reg in regs.into_iter() {
                 console::log_1(&JsValue::from(format!(
                     "  {:?}: {}",
                     reg.subjects(),
@@ -605,7 +636,7 @@ impl Assembly {
     pub fn realize(&self) {
         // index the elements
         self.elements.update_silent(|elts| {
-            for (index, (_, elt)) in elts.into_iter().enumerate() {
+            for (index, elt) in elts.iter().enumerate() {
                 elt.set_column_index(index);
             }
         });
@@ -613,11 +644,11 @@ impl Assembly {
         // set up the constraint problem
         let problem = self.elements.with_untracked(|elts| {
             let mut problem = ConstraintProblem::new(elts.len());
-            for (_, elt) in elts {
+            for elt in elts {
                 elt.pose(&mut problem);
             }
             self.regulators.with_untracked(|regs| {
-                for (_, reg) in regs {
+                for reg in regs {
                     reg.pose(&mut problem);
                 }
             });
@@ -660,7 +691,7 @@ impl Assembly {
         
         if success {
             // read out the solution
-            for (_, elt) in self.elements.get_clone_untracked() {
+            for elt in self.elements.get_clone_untracked() {
                 elt.representation().update(
                     |rep| rep.set_column(0, &config.column(elt.column_index().unwrap()))
                 );
@@ -741,7 +772,7 @@ impl Assembly {
         // normalizations, so we restore those afterward
         /* KLUDGE */
         // for now, we only restore the normalizations of spheres
-        for (_, elt) in self.elements.get_clone_untracked() {
+        for elt in self.elements.get_clone_untracked() {
             elt.representation().update_silent(|rep| {
                 match elt.column_index() {
                     Some(column_index) => {
diff --git a/app-proto/src/display.rs b/app-proto/src/display.rs
index c6a5441..a2fe4b6 100644
--- a/app-proto/src/display.rs
+++ b/app-proto/src/display.rs
@@ -363,7 +363,7 @@ pub fn Display() -> View {
     let scene_changed = create_signal(true);
     create_effect(move || {
         state.assembly.elements.with(|elts| {
-            for (_, elt) in elts {
+            for elt in elts {
                 elt.representation().track();
             }
         });
@@ -616,7 +616,7 @@ pub fn Display() -> View {
                 
                 // set up the scene
                 state.assembly.elements.with_untracked(
-                    |elts| for (_, elt) in elts {
+                    |elts| for elt in elts {
                         let selected = state.selection.with(|sel| sel.contains(elt));
                         elt.show(&mut scene, selected);
                     }
@@ -851,7 +851,7 @@ pub fn Display() -> View {
                 let (dir, pixel_size) = event_dir(&event);
                 console::log_1(&JsValue::from(dir.to_string()));
                 let mut clicked: Option<(Rc<dyn Element>, f64)> = None;
-                for (_, elt) in state.assembly.elements.get_clone_untracked() {
+                for elt in state.assembly.elements.get_clone_untracked() {
                     match assembly_to_world.with(|asm_to_world| elt.cast(dir, asm_to_world, pixel_size)) {
                         Some(depth) => match clicked {
                             Some((_, best_depth)) => {
diff --git a/app-proto/src/outline.rs b/app-proto/src/outline.rs
index 0c852b4..caf11e8 100644
--- a/app-proto/src/outline.rs
+++ b/app-proto/src/outline.rs
@@ -228,11 +228,15 @@ pub fn Outline() -> View {
     let state = use_context::<AppState>();
     
     // list the elements alphabetically by ID
+    /* TO DO */
+    // this code is designed to generalize easily to other sort keys. if we only
+    // ever wanted to sort by ID, we could do that more simply using the
+    // `elements_by_id` index
     let element_list = state.assembly.elements.map(
         |elts| elts
             .clone()
             .into_iter()
-            .sorted_by_key(|(_, elt)| elt.id().clone())
+            .sorted_by_key(|elt| elt.id().clone())
             .collect()
     );
     
@@ -246,10 +250,10 @@ pub fn Outline() -> View {
         ) {
             Keyed(
                 list=element_list,
-                view=|(_, elt)| view! {
+                view=|elt| view! {
                     ElementOutlineItem(element=elt)
                 },
-                key=|(_, elt)| elt.serial()
+                key=|elt| elt.serial()
             )
         }
     }