diff --git a/compiler/gen_wasm/src/backend.rs b/compiler/gen_wasm/src/backend.rs
index 529715115d..74d76c0260 100644
--- a/compiler/gen_wasm/src/backend.rs
+++ b/compiler/gen_wasm/src/backend.rs
@@ -170,6 +170,10 @@ impl<'a> WasmBackend<'a> {
     #[cfg(not(debug_assertions))]
     pub fn register_symbol_debug_names(&self) {}
 
+    pub fn get_fn_table_index(&mut self, fn_index: u32) -> i32 {
+        self.module.element.get_fn_table_index(fn_index)
+    }
+
     /// Create an IR Symbol for an anonymous value (such as ListLiteral)
     pub fn create_symbol(&mut self, debug_name: &str) -> Symbol {
         let ident_ids = self
diff --git a/compiler/gen_wasm/src/low_level.rs b/compiler/gen_wasm/src/low_level.rs
index 2fc2fcefc3..20f719b6bd 100644
--- a/compiler/gen_wasm/src/low_level.rs
+++ b/compiler/gen_wasm/src/low_level.rs
@@ -8,8 +8,7 @@ use roc_mono::layout::{Builtin, Layout, UnionLayout};
 use roc_mono::low_level::HigherOrder;
 
 use crate::backend::{ProcLookupData, ProcSource, WasmBackend};
-use crate::layout::CallConv;
-use crate::layout::{StackMemoryFormat, WasmLayout};
+use crate::layout::{CallConv, StackMemoryFormat, WasmLayout};
 use crate::storage::{StackMemoryLocation, StoredValue};
 use crate::wasm_module::{Align, ValueType};
 use crate::TARGET_INFO;
@@ -1010,6 +1009,9 @@ pub fn call_higher_order_lowlevel<'a>(
     let wrapper_fn_idx = backend.register_helper_proc(wrapper_sym, wrapper_layout, source);
     let inc_fn_idx = backend.gen_refcount_inc_for_zig(closure_data_layout);
 
+    let wrapper_fn_ptr = backend.get_fn_table_index(wrapper_fn_idx);
+    let inc_fn_ptr = backend.get_fn_table_index(inc_fn_idx);
+
     match op {
         // List.map : List elem_old, (elem_old -> elem_new) -> List elem_new
         ListMap { xs } => {
@@ -1030,13 +1032,13 @@ pub fn call_higher_order_lowlevel<'a>(
             // Load return pointer & argument values
             backend.storage.load_symbols(cb, &[return_sym]);
             backend.storage.load_symbol_zig(cb, *xs);
-            cb.i32_const(wrapper_fn_idx as i32);
+            cb.i32_const(wrapper_fn_ptr);
             if closure_data_exists {
                 backend.storage.load_symbols(cb, &[*captured_environment]);
             } else {
                 cb.i32_const(0); // null pointer
             }
-            cb.i32_const(inc_fn_idx as i32);
+            cb.i32_const(inc_fn_ptr);
             cb.i32_const(*owns_captured_environment as i32);
             cb.i32_const(elem_new_align as i32); // used for allocating the new list
             cb.i32_const(elem_old_size as i32);
diff --git a/compiler/gen_wasm/src/wasm_module/sections.rs b/compiler/gen_wasm/src/wasm_module/sections.rs
index 4d30809e1f..f622bef579 100644
--- a/compiler/gen_wasm/src/wasm_module/sections.rs
+++ b/compiler/gen_wasm/src/wasm_module/sections.rs
@@ -805,7 +805,7 @@ enum ElementSegmentFormatId {
 
 #[derive(Debug)]
 struct ElementSegment<'a> {
-    offset: ConstExpr,
+    offset: ConstExpr, // The starting table index for the segment
     fn_indices: Vec<'a, u32>,
 }
 
@@ -856,6 +856,9 @@ impl<'a> Serialize for ElementSegment<'a> {
     }
 }
 
+/// An "element" represents an indirectly-callable function the Wasm runtime's function table.
+/// Future Wasm versions might have tables where the elements are DOM references or other things.
+/// Elements can be initialised in groups called "segments". Normally there's just one.
 #[derive(Debug)]
 pub struct ElementSection<'a> {
     segments: Vec<'a, ElementSegment<'a>>,
@@ -867,15 +870,41 @@ impl<'a> ElementSection<'a> {
     pub fn preload(arena: &'a Bump, module_bytes: &[u8], cursor: &mut usize) -> Self {
         let (num_segments, body_bytes) = parse_section(Self::ID, module_bytes, cursor);
 
-        let mut segments = Vec::with_capacity_in(num_segments as usize, arena);
+        if num_segments == 0 {
+            let seg = ElementSegment {
+                offset: ConstExpr::I32(1),
+                fn_indices: bumpalo::vec![in arena],
+            };
+            ElementSection {
+                segments: bumpalo::vec![in arena; seg],
+            }
+        } else {
+            let mut segments = Vec::with_capacity_in(num_segments as usize, arena);
 
-        let mut body_cursor = 0;
-        for _ in 0..num_segments {
-            let seg = ElementSegment::parse(arena, body_bytes, &mut body_cursor);
-            segments.push(seg);
+            let mut body_cursor = 0;
+            for _ in 0..num_segments {
+                let seg = ElementSegment::parse(arena, body_bytes, &mut body_cursor);
+                segments.push(seg);
+            }
+            ElementSection { segments }
         }
+    }
 
-        ElementSection { segments }
+    /// Get a table index for a function (equivalent to a function pointer)
+    /// The function will be inserted into the table if it's not already there.
+    /// This index is what the call_indirect instruction expects
+    /// (It works mostly the same as with pointers, except you can't jump to arbitrary code)
+    pub fn get_fn_table_index(&mut self, fn_index: u32) -> i32 {
+        // In practice there is always one segment. We allow a bit more generality by using the last one.
+        let segment = self.segments.last_mut().unwrap();
+        let pos = segment.fn_indices.iter().position(|f| *f == fn_index);
+        if let Some(existing_table_index) = pos {
+            existing_table_index as i32
+        } else {
+            let new_table_index = segment.fn_indices.len();
+            segment.fn_indices.push(fn_index);
+            new_table_index as i32
+        }
     }
 
     pub fn size(&self) -> usize {