diff --git a/Sources/MultiArray/ArrayData.swift b/Sources/MultiArray/ArrayData.swift
index d683d6f..b4686b6 100644
--- a/Sources/MultiArray/ArrayData.swift
+++ b/Sources/MultiArray/ArrayData.swift
@@ -18,8 +18,8 @@
 public protocol ArrayData {
     associatedtype Buffer
 
-    static func initialise(_ arrayData: Buffer, at: Int, to value: Self)
-    static func deinitialise(_ arrayData: Buffer, count: Int)
+    static func initialize(_ arrayData: Buffer, at: Int, to value: Self)
+    static func deinitialize(_ arrayData: Buffer, count: Int)
 
     static func read(_ arrayData: Buffer, at index: Int) -> Self
     static func write(_ arrayData: Buffer, at index: Int, to value: Self)
@@ -32,12 +32,12 @@ public protocol ArrayData {
 // references (i.e. machine types)
 extension ArrayData where Buffer == UnsafeMutablePointer<Self> {
     @inlinable
-    public static func initialise(_ arrayData: Self.Buffer, at index: Int, to value: Self) {
+    public static func initialize(_ arrayData: Self.Buffer, at index: Int, to value: Self) {
         (arrayData + index).initialize(to: value)
     }
 
     @inlinable
-    public static func deinitialise(_: Self.Buffer, count _: Int) { /* no-op */ }
+    public static func deinitialize(_: Self.Buffer, count _: Int) { /* no-op */ }
 
     @inlinable
     // @inline(__always)
@@ -113,10 +113,10 @@ extension Unit: ArrayData {
     public typealias Buffer = Void
 
     @inlinable
-    public static func initialise(_: Self.Buffer, at _: Int, to _: Self) { /* no-op */ }
+    public static func initialize(_: Self.Buffer, at _: Int, to _: Self) { /* no-op */ }
 
     @inlinable
-    public static func deinitialise(_: Self.Buffer, count _: Int) { /* no-op */ }
+    public static func deinitialize(_: Self.Buffer, count _: Int) { /* no-op */ }
 
     @inlinable
     // @inline(__always)
@@ -146,12 +146,12 @@ extension Box: ArrayData {
     public typealias Buffer = UnsafeMutablePointer<Element>
 
     @inlinable
-    public static func initialise(_ arrayData: Self.Buffer, at index: Int, to value: Self) {
+    public static func initialize(_ arrayData: Self.Buffer, at index: Int, to value: Self) {
         (arrayData + index).initialize(to: value.unbox)
     }
 
     @inlinable
-    public static func deinitialise(_ arrayData: Self.Buffer, count: Int) {
+    public static func deinitialize(_ arrayData: Self.Buffer, count: Int) {
         arrayData.deinitialize(count: count)
     }
 
@@ -192,15 +192,15 @@ extension Product: ArrayData where A: ArrayData, B: ArrayData {
     public typealias Buffer = (A.Buffer, B.Buffer)
 
     @inlinable
-    public static func initialise(_ arrayData: Self.Buffer, at index: Int, to value: Self) {
-        A.initialise(arrayData.0, at: index, to: value._0)
-        B.initialise(arrayData.1, at: index, to: value._1)
+    public static func initialize(_ arrayData: Self.Buffer, at index: Int, to value: Self) {
+        A.initialize(arrayData.0, at: index, to: value._0)
+        B.initialize(arrayData.1, at: index, to: value._1)
     }
 
     @inlinable
-    public static func deinitialise(_ arrayData: Self.Buffer, count: Int) {
-        A.deinitialise(arrayData.0, count: count)
-        B.deinitialise(arrayData.1, count: count)
+    public static func deinitialize(_ arrayData: Self.Buffer, count: Int) {
+        A.deinitialize(arrayData.0, count: count)
+        B.deinitialize(arrayData.1, count: count)
     }
 
     @inlinable
diff --git a/Sources/MultiArray/MultiArray.swift b/Sources/MultiArray/MultiArray.swift
index 06aeacb..ba70dd1 100644
--- a/Sources/MultiArray/MultiArray.swift
+++ b/Sources/MultiArray/MultiArray.swift
@@ -34,11 +34,23 @@ public struct MultiArray<Element> where Element: Generic, Element.RawRepresentat
     /// produce each value.
     @inlinable
     public init(count: Int, with generator: (Int) throws -> Element) rethrows {
-        precondition(count >= 0)
-        self.arrayData = .init(unsafeUninitializedCapacity: count)
-        for i in 0 ..< count {
-            let value = try generator(i)
-            Element.RawRepresentation.initialise(self.arrayData.storage, at: i, to: value.rawRepresentation)
+        try self.init(unsafeUninitializedCapacity: count) { buffer in
+            for i in 0 ..< count {
+                let value = try generator(i)
+                buffer.initializeElement(at: i, to: value)
+            }
+        }
+    }
+
+    /// Create a new MultiArray by applying the given function to each index to
+    /// produce each value.
+    @inlinable
+    public init<E: Error>(count: Int, with generator: (Int) throws(E) -> Element) throws(E) {
+        try self.init(unsafeUninitializedCapacity: count) { buffer throws(E) in
+            for i in 0 ..< count {
+                let value = try generator(i)
+                buffer.initializeElement(at: i, to: value)
+            }
         }
     }
 
@@ -66,6 +78,37 @@ public struct MultiArray<Element> where Element: Generic, Element.RawRepresentat
             self.init(Array(elements))
         }
     }
+
+    /// Creates an array with the specified capacity, then calls the given
+    /// closure with a buffer covering the array's uninitialized memory.
+    @inlinable
+    public init<E: Error>(
+        unsafeUninitializedCapacity count: Int,
+        initializingWith: (inout UninitializedMultiArrayData<Element>) throws(E) -> Void
+    ) throws(E) {
+        precondition(count >= 0)
+        self.arrayData = .init(unsafeUninitializedCapacity: count)
+        var buffer = UninitializedMultiArrayData<Element>(arrayData.storage)
+        try initializingWith(&buffer)
+    }
+}
+
+// Wrapper so that we can expose the buffer using the surface Element type,
+// rather than the underlying RawRepresentation type.
+public struct UninitializedMultiArrayData<Element> where Element: Generic, Element.RawRepresentation: ArrayData {
+    @usableFromInline
+    let storage: Element.RawRepresentation.Buffer
+
+    @usableFromInline
+    init(_ storage: Element.RawRepresentation.Buffer) {
+        self.storage = storage
+    }
+
+    /// Initialises the element at the given `index` to the given `value`
+    @inlinable
+    public func initializeElement(at index: Int, to value: consuming Element) {
+        Element.RawRepresentation.initialize(self.storage, at: index, to: value.rawRepresentation)
+    }
 }
 
 // TODO: It would be better if this is generic over the underlying storage
@@ -79,12 +122,12 @@ internal final class MultiArrayData<A: ArrayData> {
     let count: Int
 
     @usableFromInline
-    var context: UnsafeMutableRawPointer
+    let context: UnsafeMutableRawPointer
 
     // Storing the internal pointers for speed(?), but we could also recompute
     // them from the base context.
     @usableFromInline
-    var storage: A.Buffer
+    let storage: A.Buffer
 
     @inlinable
     init(unsafeUninitializedCapacity count: Int) {
@@ -106,7 +149,7 @@ internal final class MultiArrayData<A: ArrayData> {
     }
 
     deinit {
-        A.deinitialise(self.storage, count: self.count)
+        A.deinitialize(self.storage, count: self.count)
         self.context.deallocate()
     }
 }