diff --git a/src/field.rs b/src/field.rs
index 2241c13..9d8d041 100644
--- a/src/field.rs
+++ b/src/field.rs
@@ -96,17 +96,10 @@ impl FieldElement {
 
     /// Compute (self^(2^250-1), self^11), used as a helper function
     /// within invert() and pow22523().
-    ///
-    /// XXX This returns an extra intermediate to save computation in
-    /// finding inverses, at the cost of an extra copy when it's not
-    /// used (e.g., when raising to (p-1)/2 or (p-5)/8). Good idea?
     fn pow22501(&self) -> (FieldElement, FieldElement) {
         // Instead of managing which temporary variables are used
-        // for what, we define as many as we need and trust the
-        // compiler to reuse stack space as appropriate.
-        //
-        // XXX testing some examples suggests that this does happen,
-        // but it would be good to check asm for this function.
+        // for what, we define as many as we need and leave stack
+        // allocation to the compiler
         //
         // Each temporary variable t_i is of the form (self)^e_i.
         // Squaring t_i corresponds to multiplying e_i by 2,
@@ -177,12 +170,9 @@ impl FieldElement {
     ///
     /// The inverse is computed as self^(p-2), since
     /// x^(p-2)x = x^(p-1) = 1 (mod p).
-    //
-    // XXX do we want the debug assertion to check for zero? it breaks behaviour
-    // such as that such as in curve25519_dalek::montgomery::test::identity_to_monty.
+    ///
+    /// This function returns zero on input zero.
     pub fn invert(&self) -> FieldElement {
-        // debug_assert!(*self != FieldElement::zero());
-
         // The bits of p-2 = 2^255 -19 -2 are 11010111111...11.
         //
         //                                 nonzero bits of exponent
@@ -194,8 +184,7 @@ impl FieldElement {
     }
 
     /// Raise this field element to the power (p-5)/8 = 2^252 -3.
-    /// Used in decoding.
-    pub fn pow_p58(&self) -> FieldElement {
+    fn pow_p58(&self) -> FieldElement {
         // The bits of (p-5)/8 are 101111.....11.
         //
         //                                 nonzero bits of exponent