diff --git a/build.rs b/build.rs
index ee90958..fe4b1fe 100644
--- a/build.rs
+++ b/build.rs
@@ -24,39 +24,26 @@ use std::path::Path;
 #[cfg(feature = "serde")]
 extern crate serde;
 
-#[path="src/field.rs"]
-mod field;
-#[cfg(not(feature="radix_51"))]
-#[path="src/field_32bit.rs"]
-mod field_32bit;
-#[cfg(feature="radix_51")]
-#[path="src/field_64bit.rs"]
-mod field_64bit;
+// Public modules
 
 #[path="src/scalar.rs"]
 mod scalar;
-#[cfg(not(feature="radix_51"))]
-#[path="src/scalar_32bit.rs"]
-mod scalar_32bit;
-#[cfg(feature="radix_51")]
-#[path="src/scalar_64bit.rs"]
-mod scalar_64bit;
-
 #[path="src/montgomery.rs"]
 mod montgomery;
 #[path="src/edwards.rs"]
 mod edwards;
 #[path="src/ristretto.rs"]
 mod ristretto;
-
 #[path="src/constants.rs"]
 mod constants;
-#[cfg(not(feature="radix_51"))]
-#[path="src/constants_32bit.rs"]
-mod constants_32bit;
-#[cfg(feature="radix_51")]
-#[path="src/constants_64bit.rs"]
-mod constants_64bit;
+
+// Internal modules
+
+#[path="src/field.rs"]
+mod field;
+
+#[path="src/backend/mod.rs"]
+mod backend;
 
 use edwards::EdwardsBasepointTable;
 
@@ -73,10 +60,10 @@ fn main() {
 
     f.write_all(format!("\n
 #[cfg(feature=\"radix_51\")]
-use field_64bit::FieldElement64;
+use backend::u64::field::FieldElement64;
 
 #[cfg(not(feature=\"radix_51\"))]
-use field_32bit::FieldElement32;
+use backend::u32::field::FieldElement32;
 
 use edwards::AffineNielsPoint;
 use edwards::EdwardsBasepointTable;
diff --git a/src/backend/mod.rs b/src/backend/mod.rs
new file mode 100644
index 0000000..3947fb9
--- /dev/null
+++ b/src/backend/mod.rs
@@ -0,0 +1,32 @@
+// -*- mode: rust; -*-
+//
+// This file is part of curve25519-dalek.
+// Copyright (c) 2016-2017 Isis Lovecruft, Henry de Valence
+// See LICENSE for licensing information.
+//
+// Authors:
+// - Isis Agora Lovecruft <isis@patternsinthevoid.net>
+// - Henry de Valence <hdevalence@hdevalence.ca>
+
+//! This module contains "backends" that contain different
+//! implementations of common code for different architectures.
+//!
+//! The naming of the `u32` and `u64` modules is somewhat unfortunate,
+//! since these are also the names of primitive types.  Since types have
+//! a different namespace than modules, this isn't a problem to the
+//! compiler, but it could cause confusion.
+//!
+//! However, it's unlikely that the names of those modules would be
+//! brought into scope directly, instead of used as
+//! `backend::u32::field` or similar.  Unfortunately we can't use
+//! `32bit` since identifiers can't start with letters, and the backends
+//! do use `u32`/`u64`, so this seems like a least-bad option.
+
+/// Code using `u32`s and a `(u32, u32) -> u64` multiplier.
+#[cfg(not(feature="radix_51"))]
+pub mod u32;
+
+/// Code using `u64`s and a `(u64, u64) -> u128` multiplier.
+#[cfg(feature="radix_51")]
+pub mod u64;
+
diff --git a/src/constants_32bit.rs b/src/backend/u32/constants.rs
similarity index 98%
rename from src/constants_32bit.rs
rename to src/backend/u32/constants.rs
index 740abc5..2600c64 100644
--- a/src/constants_32bit.rs
+++ b/src/backend/u32/constants.rs
@@ -12,8 +12,8 @@
 //! and useful field elements like `sqrt(-1)`), as well as
 //! lookup tables of pre-computed points.
 
-use field_32bit::FieldElement32;
-use scalar_32bit::Scalar32;
+use backend::u32::field::FieldElement32;
+use backend::u32::scalar::Scalar32;
 use edwards::ExtendedPoint;
 
 /// Edwards `d` value, equal to `-121665/121666 mod p`.
diff --git a/src/field_32bit.rs b/src/backend/u32/field.rs
similarity index 100%
rename from src/field_32bit.rs
rename to src/backend/u32/field.rs
diff --git a/src/backend/u32/mod.rs b/src/backend/u32/mod.rs
new file mode 100644
index 0000000..fa54a15
--- /dev/null
+++ b/src/backend/u32/mod.rs
@@ -0,0 +1,15 @@
+// -*- mode: rust; -*-
+//
+// This file is part of curve25519-dalek.
+// Copyright (c) 2016-2017 Isis Lovecruft, Henry de Valence
+// See LICENSE for licensing information.
+//
+// Authors:
+// - Isis Agora Lovecruft <isis@patternsinthevoid.net>
+// - Henry de Valence <hdevalence@hdevalence.ca>
+
+pub mod field;
+
+pub mod scalar;
+
+pub mod constants;
\ No newline at end of file
diff --git a/src/scalar_32bit.rs b/src/backend/u32/scalar.rs
similarity index 100%
rename from src/scalar_32bit.rs
rename to src/backend/u32/scalar.rs
diff --git a/src/constants_64bit.rs b/src/backend/u64/constants.rs
similarity index 98%
rename from src/constants_64bit.rs
rename to src/backend/u64/constants.rs
index c9d6b4a..3af570c 100644
--- a/src/constants_64bit.rs
+++ b/src/backend/u64/constants.rs
@@ -12,8 +12,8 @@
 //! and useful field elements like `sqrt(-1)`), as well as
 //! lookup tables of pre-computed points.
 
-use field_64bit::FieldElement64;
-use scalar_64bit::Scalar64;
+use backend::u64::field::FieldElement64;
+use backend::u64::scalar::Scalar64;
 use edwards::ExtendedPoint;
 
 /// Edwards `d` value, equal to `-121665/121666 mod p`.
diff --git a/src/field_64bit.rs b/src/backend/u64/field.rs
similarity index 99%
rename from src/field_64bit.rs
rename to src/backend/u64/field.rs
index 807bba8..3c6d4f0 100644
--- a/src/field_64bit.rs
+++ b/src/backend/u64/field.rs
@@ -25,10 +25,6 @@ use core::ops::Neg;
 
 use subtle::ConditionallyAssignable;
 
-/// In the 64-bit implementation, field elements are represented in
-/// radix 2^51 as five `u64`s.
-pub type Limb = u64;
-
 /// A `FieldElement64` represents an element of the field GF(2^255 - 19).
 ///
 /// In the 64-bit implementation, a `FieldElement` is represented in
diff --git a/src/backend/u64/mod.rs b/src/backend/u64/mod.rs
new file mode 100644
index 0000000..fa54a15
--- /dev/null
+++ b/src/backend/u64/mod.rs
@@ -0,0 +1,15 @@
+// -*- mode: rust; -*-
+//
+// This file is part of curve25519-dalek.
+// Copyright (c) 2016-2017 Isis Lovecruft, Henry de Valence
+// See LICENSE for licensing information.
+//
+// Authors:
+// - Isis Agora Lovecruft <isis@patternsinthevoid.net>
+// - Henry de Valence <hdevalence@hdevalence.ca>
+
+pub mod field;
+
+pub mod scalar;
+
+pub mod constants;
\ No newline at end of file
diff --git a/src/scalar_64bit.rs b/src/backend/u64/scalar.rs
similarity index 100%
rename from src/scalar_64bit.rs
rename to src/backend/u64/scalar.rs
diff --git a/src/constants.rs b/src/constants.rs
index 6434f89..3ba6ce4 100644
--- a/src/constants.rs
+++ b/src/constants.rs
@@ -36,9 +36,9 @@ use montgomery::CompressedMontgomeryU;
 use scalar::Scalar;
 
 #[cfg(feature="radix_51")]
-pub use constants_64bit::*;
+pub use backend::u64::constants::*;
 #[cfg(not(feature="radix_51"))]
-pub use constants_32bit::*;
+pub use backend::u32::constants::*;
 
 /// Basepoint has y = 4/5.
 ///
@@ -138,7 +138,7 @@ mod test {
     #[test]
     #[cfg(feature="radix_51")]
     fn sqrt_minus_aplus2() {
-        use field_64bit::FieldElement64;
+        use backend::u64::field::FieldElement64;
         let minus_aplus2 = -&FieldElement64([486664,0,0,0,0]);
         let sqrt = constants::SQRT_MINUS_APLUS2;
         let sq = &sqrt * &sqrt;
@@ -150,7 +150,7 @@ mod test {
     #[test]
     #[cfg(not(feature="radix_51"))]
     fn sqrt_minus_aplus2() {
-        use field_32bit::FieldElement32;
+        use backend::u32::field::FieldElement32;
         let minus_aplus2 = -&FieldElement32([486664,0,0,0,0,0,0,0,0,0]);
         let sqrt = constants::SQRT_MINUS_APLUS2;
         let sq = &sqrt * &sqrt;
@@ -180,7 +180,7 @@ mod test {
     #[cfg(not(feature="radix_51"))]
     #[test]
     fn test_d_vs_ratio() {
-        use field_32bit::FieldElement32;
+        use backend::u32::field::FieldElement32;
         let a = -&FieldElement32([121665,0,0,0,0,0,0,0,0,0]);
         let b =   FieldElement32([121666,0,0,0,0,0,0,0,0,0]);
         let d = &a * &b.invert();
@@ -193,7 +193,7 @@ mod test {
     #[cfg(feature="radix_51")]
     #[test]
     fn test_d_vs_ratio() {
-        use field_64bit::FieldElement64;
+        use backend::u64::field::FieldElement64;
         let a = -&FieldElement64([121665,0,0,0,0]);
         let b =   FieldElement64([121666,0,0,0,0]);
         let d = &a * &b.invert();
diff --git a/src/field.rs b/src/field.rs
index 9464fa3..86f9aad 100644
--- a/src/field.rs
+++ b/src/field.rs
@@ -27,17 +27,19 @@ use subtle::ConditionallyNegatable;
 use subtle::Equal;
 
 use constants;
+use backend;
 
+#[cfg(feature="radix_51")]
+pub use backend::u64::field::*;
 /// A `FieldElement` represents an element of the field GF(2^255 - 19).
 #[cfg(feature="radix_51")]
-pub type FieldElement = FieldElement64;
+pub type FieldElement = backend::u64::field::FieldElement64;
+
+#[cfg(not(feature="radix_51"))]
+pub use backend::u32::field::*;
 /// A `FieldElement` represents an element of the field GF(2^255 - 19).
 #[cfg(not(feature="radix_51"))]
-pub type FieldElement = FieldElement32;
-#[cfg(feature="radix_51")]
-pub use field_64bit::*;
-#[cfg(not(feature="radix_51"))]
-pub use field_32bit::*;
+pub type FieldElement = backend::u32::field::FieldElement32;
 
 impl Eq for FieldElement {}
 impl PartialEq for FieldElement {
diff --git a/src/lib.rs b/src/lib.rs
index 38593c4..1834835 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -35,22 +35,9 @@
 //! hatred of the Daleks.  Rusty destroys the other Daleks and departs the
 //! ship, determined to track down and bring an end to the Dalek race.
 
-#[cfg(all(test, feature = "bench"))]
-extern crate test;
-
-// this appears to only be used for serde support right now?
-#[cfg(feature = "serde")]
-#[macro_use]
-extern crate arrayref;
-
-extern crate generic_array;
-extern crate digest;
-extern crate subtle;
-
-#[cfg(feature = "serde")]
-extern crate serde;
-#[cfg(all(test, feature = "serde"))]
-extern crate serde_cbor;
+//------------------------------------------------------------------------
+// External dependencies:
+//------------------------------------------------------------------------
 
 #[cfg(feature = "std")]
 extern crate core;
@@ -61,29 +48,51 @@ extern crate rand;
 #[cfg(feature = "alloc")]
 extern crate alloc;
 
-// Modules for low-level operations directly on field elements and curve points.
+#[cfg(all(test, feature = "bench"))]
+extern crate test;
 
-pub mod field;
-#[cfg(not(feature="radix_51"))]
-mod field_32bit;
-#[cfg(feature="radix_51")]
-mod field_64bit;
+// The `Digest` trait is implemented using `generic_array`, so we need it too. Hopefully we can eliminate `generic_array` from `Digest` once const generics land.
+extern crate digest;
+extern crate generic_array;
 
+// Used for traits related to constant-time code.
+extern crate subtle;
+
+#[cfg(feature = "serde")]
+extern crate serde;
+#[cfg(all(test, feature = "serde"))]
+extern crate serde_cbor;
+
+// this appears to only be used for serde support right now?
+// XXX let's eliminate this dep
+#[cfg(feature = "serde")]
+#[macro_use]
+extern crate arrayref;
+
+//------------------------------------------------------------------------
+// curve25519-dalek public modules
+//------------------------------------------------------------------------
+
+// Scalar arithmetic mod l = 2^252 + ..., the order of the Ristretto group
 pub mod scalar;
-#[cfg(not(feature="radix_51"))]
-mod scalar_32bit;
-#[cfg(feature="radix_51")]
-mod scalar_64bit;
-
-pub mod edwards;
+// Point operations on the Montgomery form of Curve25519
 pub mod montgomery;
-
+// Point operations on the Edwards form of Curve25519
+pub mod edwards;
+// Group operations on the Ristretto group
 pub mod ristretto;
-
-// Low-level curve and point constants, as well as pre-computed curve group elements.
-
+// Useful constants, like the Ed25519 basepoint
 pub mod constants;
-#[cfg(not(feature="radix_51"))]
-mod constants_32bit;
-#[cfg(feature="radix_51")]
-mod constants_64bit;
+
+//------------------------------------------------------------------------
+// curve25519-dalek internal modules
+//------------------------------------------------------------------------
+
+// Finite field arithmetic mod p = 2^255 - 19
+pub(crate) mod field;
+
+// Arithmetic backends (using u32, u64, etc) live here
+pub(crate) mod backend;
+
+// Internal curve models which are not part of the public API.
+//mod curve_models;
\ No newline at end of file
diff --git a/src/scalar.rs b/src/scalar.rs
index c793cc3..e5fa102 100644
--- a/src/scalar.rs
+++ b/src/scalar.rs
@@ -46,6 +46,17 @@ use subtle::slices_equal;
 use subtle::ConditionallyAssignable;
 use subtle::Equal;
 
+use backend;
+
+/// An `UnpackedScalar` represents an element of the field GF(l), optimized for speed.
+#[cfg(feature="radix_51")]
+type UnpackedScalar = backend::u64::scalar::Scalar64;
+
+/// An `UnpackedScalar` represents an element of the field GF(l), optimized for speed.
+#[cfg(not(feature="radix_51"))]
+type UnpackedScalar = backend::u32::scalar::Scalar32;
+
+
 /// The `Scalar` struct represents an element in ℤ/lℤ, where
 ///
 /// l = 2^252 + 27742317777372353535851937790883648493
@@ -227,18 +238,6 @@ impl<'de> Deserialize<'de> for Scalar {
     }
 }
 
-/// An `UnpackedScalar` represents an element of the field GF(l), optimized for speed.
-#[cfg(feature="radix_51")]
-type UnpackedScalar = Scalar64;
-#[cfg(feature="radix_51")]
-use scalar_64bit::*;
-
-/// An `UnpackedScalar` represents an element of the field GF(l), optimized for speed.
-#[cfg(not(feature="radix_51"))]
-type UnpackedScalar = Scalar32;
-#[cfg(not(feature="radix_51"))]
-use scalar_32bit::*;
-
 impl Scalar {
     /// Return a `Scalar` chosen uniformly at random using a user-provided RNG.
     ///