diff --git a/src/aal/aal.h b/src/aal/aal.h
index 55b1477..c6bab95 100644
--- a/src/aal/aal.h
+++ b/src/aal/aal.h
@@ -46,6 +46,31 @@ namespace snmalloc
   template<class Arch>
   struct AAL_Generic : Arch
   {
+    /*
+     * Provide a default specification of address_t as uintptr_t for Arch-es
+     * that support IntegerPointers.  Those Arch-es without IntegerPoihnters
+     * must explicitly give their address_t.
+     *
+     * This somewhat obtuse way of spelling the defaulting is necessary so
+     * that all arguments to std::conditional_t are valid, even if they
+     * wouldn't be valid in context.  One might rather wish to say
+     *
+     *   std::conditional_t<..., uintptr_t, Arch::address_t>
+     *
+     * but that requires that Arch::address_t always be given, precisely
+     * the thing we're trying to avoid with the conditional.
+     */
+
+    struct default_address_t
+    {
+      using address_t = uintptr_t;
+    };
+
+    using address_t = typename std::conditional_t<
+      (Arch::aal_features & IntegerPointers) != 0,
+      default_address_t,
+      Arch>::address_t;
+
     /**
      * Prefetch a specific address.
      *
diff --git a/src/ds/address.h b/src/ds/address.h
index 720f1af..c1c837d 100644
--- a/src/ds/address.h
+++ b/src/ds/address.h
@@ -13,7 +13,7 @@ namespace snmalloc
    * separated into two types, one for raw addresses and one for addresses that
    * can be cast back to pointers.
    */
-  using address_t = uintptr_t;
+  using address_t = Aal::address_t;
 
   /**
    * Perform pointer arithmetic and return the adjusted pointer.