diff --git a/NOTES b/NOTES
index edee9d0594059f74dc64e92b52c6f680971c26f1..f1ea86b242fe76435192f0cdf24f922364970746 100644
--- a/NOTES
+++ b/NOTES
@@ -15,6 +15,20 @@ consistency checks.
 
 TODO: Add consistency check to the bitreader
 
-We should support the use of parse-table-based parse methods; add a
-parse_compile method that must be called before the newly-created
-parser is used.
+TODO: We should support the use of parse-table-based parse methods; add a
+      parse_compile method that must be called before the newly-created
+      parser is used.
+
+
+Regarding butnot and difference:
+
+There's a "do what I say, not what I do" variation in how we
+implemented these (versus how jsparse did it). His `butnot` succeeds
+if p1 and p2 both match and p1's result is longer than p2's, though
+the comments say it should succeed if p2's result is longer than
+p1's. Also, his `difference` succeeds if p1 and p2 both match, full
+stop, returning the result of p2 if p2's result is shorter than p1's
+or the result of p1 otherwise, though the comments say it should
+succeed if p2's result is shorter than p1's. Whatever; we're doing
+what the comments say.
+
diff --git a/src/hammer.c b/src/hammer.c
index 95d8a426a5fb4ef409b9f9104f327a2a8cbed190..7d1dabbcffd7ca77e1c8017e64cd502e05093100 100644
--- a/src/hammer.c
+++ b/src/hammer.c
@@ -294,7 +294,7 @@ static parse_result_t* parse_butnot(void *env, parse_state_t *state) {
   // cache the initial state of the input stream
   input_stream_t start_state = state->input_stream;
   parse_result_t *r1 = do_parse(parsers->p1, state);
-  // if r1 is null, bail out early
+  // if p1 failed, bail out early
   if (NULL == r1) {
     return NULL;
   } 
@@ -304,7 +304,7 @@ static parse_result_t* parse_butnot(void *env, parse_state_t *state) {
   parse_result_t *r2 = do_parse(parsers->p2, state);
   // TODO(mlp): I'm pretty sure the input stream state should be the post-p1 state in all cases
   state->input_stream = after_p1_state;
-  // if r2 is null, restore post-p1 state and bail out early
+  // if p2 failed, restore post-p1 state and bail out early
   if (NULL == r2) {
     return r1;
   }
@@ -326,8 +326,76 @@ const parser_t* butnot(const parser_t* p1, const parser_t* p2) {
   return ret;
 }
 
-const parser_t* difference(const parser_t* p1, const parser_t* p2) { return NULL; }
-const parser_t* xor(const parser_t* p1, const parser_t* p2) { return NULL; }
+static parse_result_t* parse_difference(void *env, parse_state_t *state) {
+  two_parsers_t *parsers = (two_parsers_t*)env;
+  // cache the initial state of the input stream
+  input_stream_t start_state = state->input_stream;
+  parse_result_t *r1 = do_parse(parsers->p1, state);
+  // if p1 failed, bail out early
+  if (NULL == r1) {
+    return NULL;
+  } 
+  // cache the state after parse #1, since we might have to back up to it
+  input_stream_t after_p1_state = state->input_stream;
+  state->input_stream = start_state;
+  parse_result_t *r2 = do_parse(parsers->p2, state);
+  // TODO(mlp): I'm pretty sure the input stream state should be the post-p1 state in all cases
+  state->input_stream = after_p1_state;
+  // if p2 failed, restore post-p1 state and bail out early
+  if (NULL == r2) {
+    return r1;
+  }
+  size_t r1len = token_length(r1);
+  size_t r2len = token_length(r2);
+  // if both match but p1's text is shorter than p2's, fail
+  if (r1len < r2len) {
+    return NULL;
+  } else {
+    return r1;
+  }
+}
+
+const parser_t* difference(const parser_t* p1, const parser_t* p2) { 
+  two_parsers_t *env = g_new(two_parsers_t, 1);
+  env->p1 = p1; env->p2 = p2;
+  parser_t *ret = g_new(parser_t, 1);
+  ret->fn = parse_difference; ret->env = (void*)env;
+  return ret;
+}
+
+static parse_result_t* parse_xor(void *env, parse_state_t *state) {
+  two_parsers_t *parsers = (two_parsers_t*)env;
+  // cache the initial state of the input stream
+  input_stream_t start_state = state->input_stream;
+  parse_result_t *r1 = do_parse(parsers->p1, state);
+  input_stream_t after_p1_state = state->input_stream;
+  // reset input stream, parse again
+  state->input_stream = start_state;
+  parse_result_t *r2 = do_parse(parsers->p2, state);
+  if (NULL == r1) {
+    if (NULL != r2) {
+      return r2;
+    } else {
+      return NULL;
+    }
+  } else {
+    if (NULL == r2) {
+      state->input_stream = after_p1_state;
+      return r1;
+    } else {
+      return NULL;
+    }
+  }
+}
+
+const parser_t* xor(const parser_t* p1, const parser_t* p2) { 
+  two_parsers_t *env = g_new(two_parsers_t, 1);
+  env->p1 = p1; env->p2 = p2;
+  parser_t *ret = g_new(parser_t, 1);
+  ret->fn = parse_xor; ret->env = (void*)env;
+  return ret;
+}
+
 const parser_t* repeat0(const parser_t* p) { return NULL; }
 const parser_t* repeat1(const parser_t* p) { return NULL; }
 const parser_t* repeat_n(const parser_t* p, const size_t n) { return NULL; }
diff --git a/src/hammer.h b/src/hammer.h
index 87252889d53212d357efcd07b10c5812258b7087..b0a9c1ab0b02cbbf5d75ccddf7af724afa0730fd 100644
--- a/src/hammer.h
+++ b/src/hammer.h
@@ -26,15 +26,7 @@
  *   input - the entire string being parsed
  *   index - current position in input
  *   length - size of input
- * THE FOLLOWING DESCRIBES HOW JSPARSE DOES IT. OUR MILEAGE MAY VARY.
- *   cache - a hash table describing the state of the parse, including partial parse_results. 
- *           It's actually a hash table of [parser_id, hash_table[index, parse_result]],
- *           where the parser id is incremented as the parse goes along (parsers that have
- *           already been applied once don't get a new parser_id ... but the global variable
- *           still increments? not sure why that is, need to debug some), and the locations
- *           at which it's been applied are memoized.
- * 
- *           In our case, it's a hash table from parser_cache_key_t to parse_state_t. 
+ *   cache - a hash table describing the state of the parse, including partial parse_results. It's a hash table from parser_cache_key_t to parse_state_t. 
  *
  */
 #define BYTE_BIG_ENDIAN 0x1
@@ -124,9 +116,22 @@ const parser_t* sequence(const parser_t* p_array[]);
 /* Given an array of parsers, p_array, apply each parser in order. The first parser to succeed is the result; if no parsers succeed, the parse fails. */
 const parser_t* choice(const parser_t* p_array[]);
 
+/* Given two parsers, p1 and p2, this parser succeeds in the following cases: 
+ * - if p1 succeeds and p2 fails
+ * - if both succeed but p1's result is shorter than p2's
+ */
 const parser_t* butnot(const parser_t* p1, const parser_t* p2);
+
+/* Given two parsers, p1 and p2, this parser succeeds in the following cases:
+ * - if p1 succeeds and p2 fails
+ * - if both succeed but p2's result is shorter than p1's
+ */
 const parser_t* difference(const parser_t* p1, const parser_t* p2);
+
+/* Given two parsers, p1 and p2, this parser succeeds if *either* p1 or p2 succeed, but not if they both do.
+ */
 const parser_t* xor(const parser_t* p1, const parser_t* p2);
+
 const parser_t* repeat0(const parser_t* p);
 const parser_t* repeat1(const parser_t* p);
 const parser_t* repeat_n(const parser_t* p, const size_t n);