diff --git a/lib/wasm/src/code_translator.rs b/lib/wasm/src/code_translator.rs
index 02cd7e1b10..681eb3b7d0 100644
--- a/lib/wasm/src/code_translator.rs
+++ b/lib/wasm/src/code_translator.rs
@@ -28,7 +28,7 @@ use cretonne::ir::condcodes::{IntCC, FloatCC};
 use cton_frontend::{ILBuilder, FunctionBuilder};
 use wasmparser::{Parser, ParserState, Operator, WasmDecoder, MemoryImmediate};
 use translation_utils::{f32_translation, f64_translation, type_to_type, translate_type, Local};
-use translation_utils::{TableIndex, SignatureIndex, FunctionIndex};
+use translation_utils::{TableIndex, SignatureIndex, FunctionIndex, MemoryIndex};
 use state::{TranslationState, ControlStackFrame};
 use std::collections::HashMap;
 use runtime::{FuncEnvironment, GlobalValue, WasmRuntime};
@@ -458,12 +458,27 @@ fn translate_operator(
          * Memory management is handled by runtime. It is usually translated into calls to
          * special functions.
          ************************************************************************************/
-        Operator::GrowMemory { reserved: _ } => {
+        Operator::GrowMemory { reserved } => {
+            // The WebAssembly MVP only supports one linear memory, but we expect the reserved
+            // argument to be a memory index.
+            let heap_index = reserved as MemoryIndex;
+            let heap = state.get_heap(builder.func, reserved, runtime);
             let val = state.pop1();
-            state.push1(runtime.translate_grow_memory(builder, val));
+            state.push1(runtime.translate_grow_memory(
+                builder.cursor(),
+                heap_index,
+                heap,
+                val,
+            ))
         }
-        Operator::CurrentMemory { reserved: _ } => {
-            state.push1(runtime.translate_current_memory(builder));
+        Operator::CurrentMemory { reserved } => {
+            let heap_index = reserved as MemoryIndex;
+            let heap = state.get_heap(builder.func, reserved, runtime);
+            state.push1(runtime.translate_current_memory(
+                builder.cursor(),
+                heap_index,
+                heap,
+            ));
         }
         /******************************* Load instructions ***********************************
          * Wasm specifies an integer alignment flag but we drop it in Cretonne.
diff --git a/lib/wasm/src/runtime/dummy.rs b/lib/wasm/src/runtime/dummy.rs
index 178d39c5d1..703b5f164a 100644
--- a/lib/wasm/src/runtime/dummy.rs
+++ b/lib/wasm/src/runtime/dummy.rs
@@ -1,8 +1,7 @@
 use runtime::{FuncEnvironment, GlobalValue, WasmRuntime};
-use translation_utils::{Local, Global, Memory, Table, GlobalIndex, TableIndex, SignatureIndex,
+use translation_utils::{Global, Memory, Table, GlobalIndex, TableIndex, SignatureIndex,
                         FunctionIndex, MemoryIndex};
-use cton_frontend::FunctionBuilder;
-use cretonne::ir::{self, Value, InstBuilder};
+use cretonne::ir::{self, InstBuilder};
 use cretonne::ir::types::*;
 use cretonne::cursor::FuncCursor;
 
@@ -88,16 +87,28 @@ impl FuncEnvironment for DummyRuntime {
     ) -> ir::Inst {
         pos.ins().call_indirect(sig_ref, callee, call_args)
     }
+
+    fn translate_grow_memory(
+        &mut self,
+        mut pos: FuncCursor,
+        _index: MemoryIndex,
+        _heap: ir::Heap,
+        _val: ir::Value,
+    ) -> ir::Value {
+        pos.ins().iconst(I32, -1)
+    }
+
+    fn translate_current_memory(
+        &mut self,
+        mut pos: FuncCursor,
+        _index: MemoryIndex,
+        _heap: ir::Heap,
+    ) -> ir::Value {
+        pos.ins().iconst(I32, -1)
+    }
 }
 
 impl WasmRuntime for DummyRuntime {
-    fn translate_grow_memory(&mut self, builder: &mut FunctionBuilder<Local>, _: Value) -> Value {
-        builder.ins().iconst(I32, -1)
-    }
-    fn translate_current_memory(&mut self, builder: &mut FunctionBuilder<Local>) -> Value {
-        builder.ins().iconst(I32, -1)
-    }
-
     fn declare_signature(&mut self, sig: &ir::Signature) {
         self.signatures.push(sig.clone());
     }
diff --git a/lib/wasm/src/runtime/spec.rs b/lib/wasm/src/runtime/spec.rs
index 5750fe5520..35f8d9ea37 100644
--- a/lib/wasm/src/runtime/spec.rs
+++ b/lib/wasm/src/runtime/spec.rs
@@ -1,10 +1,9 @@
 //! All the runtime support necessary for the wasm to cretonne translation is formalized by the
 //! trait `WasmRuntime`.
-use cton_frontend::FunctionBuilder;
-use cretonne::ir::{self, Value, InstBuilder};
+use cretonne::ir::{self, InstBuilder};
 use cretonne::cursor::FuncCursor;
-use translation_utils::{Local, SignatureIndex, FunctionIndex, TableIndex, GlobalIndex,
-                        MemoryIndex, Global, Table, Memory};
+use translation_utils::{SignatureIndex, FunctionIndex, TableIndex, GlobalIndex, MemoryIndex,
+                        Global, Table, Memory};
 
 /// The value of a WebAssembly global variable.
 #[derive(Clone, Copy)]
@@ -101,6 +100,35 @@ pub trait FuncEnvironment {
     ) -> ir::Inst {
         pos.ins().call(callee, call_args)
     }
+
+    /// Translate a `grow_memory` WebAssembly instruction.
+    ///
+    /// The `index` provided identifies the linear memory to grow, and `heap` is the heap reference
+    /// returned by `make_heap` for the same index.
+    ///
+    /// The `val` value is the requested memory size in pages.
+    ///
+    /// Returns the old size (in pages) of the memory.
+    fn translate_grow_memory(
+        &mut self,
+        pos: FuncCursor,
+        index: MemoryIndex,
+        heap: ir::Heap,
+        val: ir::Value,
+    ) -> ir::Value;
+
+    /// Translates a `current_memory` WebAssembly instruction.
+    ///
+    /// The `index` provided identifies the linear memory to query, and `heap` is the heap reference
+    /// returned by `make_heap` for the same index.
+    ///
+    /// Returns the size in pages of the memory.
+    fn translate_current_memory(
+        &mut self,
+        pos: FuncCursor,
+        index: MemoryIndex,
+        heap: ir::Heap,
+    ) -> ir::Value;
 }
 
 /// An object satisfyng the `WasmRuntime` trait can be passed as argument to the
@@ -141,8 +169,4 @@ pub trait WasmRuntime: FuncEnvironment {
     fn begin_translation(&mut self);
     /// Call this function between each function body translation.
     fn next_function(&mut self);
-    /// Translates a `grow_memory` wasm instruction. Returns the old size (in pages) of the memory.
-    fn translate_grow_memory(&mut self, builder: &mut FunctionBuilder<Local>, val: Value) -> Value;
-    /// Translates a `current_memory` wasm instruction. Returns the size in pages of the memory.
-    fn translate_current_memory(&mut self, builder: &mut FunctionBuilder<Local>) -> Value;
 }