diff --git a/include/secp256k1.h b/include/secp256k1.h
index f55a6ab9..b0a13b14 100644
--- a/include/secp256k1.h
+++ b/include/secp256k1.h
@@ -261,7 +261,7 @@ SECP256K1_DEPRECATED("Use secp256k1_context_static instead");
  *  secp256k1_context_create (or secp256k1_context_preallocated_create), which will
  *  take care of performing the self tests.
  *
- *  If the tests fail, this function will call the default error handler to abort the
+ *  If the tests fail, this function will call the default error callback to abort the
  *  program (see secp256k1_context_set_error_callback).
  */
 SECP256K1_API void secp256k1_selftest(void);
@@ -334,36 +334,37 @@ SECP256K1_API void secp256k1_context_destroy(
  *  an API call. It will only trigger for violations that are mentioned
  *  explicitly in the header.
  *
- *  The philosophy is that these shouldn't be dealt with through a
- *  specific return value, as calling code should not have branches to deal with
- *  the case that this code itself is broken.
+ *  The philosophy is that these shouldn't be dealt with through a specific
+ *  return value, as calling code should not have branches to deal with the case
+ *  that this code itself is broken.
  *
  *  On the other hand, during debug stage, one would want to be informed about
- *  such mistakes, and the default (crashing) may be inadvisable.
- *  When this callback is triggered, the API function called is guaranteed not
- *  to cause a crash, though its return value and output arguments are
- *  undefined.
+ *  such mistakes, and the default (crashing) may be inadvisable. Should this
+ *  callback return instead of crashing, the return value and output arguments
+ *  of the API function call are undefined. Moreover, the same API call may
+ *  trigger the callback again in this case.
  *
- *  When this function has not been called (or called with fn==NULL), then the
- *  default handler will be used. The library provides a default handler which
- *  writes the message to stderr and calls abort. This default handler can be
+ *  When this function has not been called (or called with fun==NULL), then the
+ *  default callback will be used. The library provides a default callback which
+ *  writes the message to stderr and calls abort. This default callback can be
  *  replaced at link time if the preprocessor macro
  *  USE_EXTERNAL_DEFAULT_CALLBACKS is defined, which is the case if the build
  *  has been configured with --enable-external-default-callbacks. Then the
  *  following two symbols must be provided to link against:
  *   - void secp256k1_default_illegal_callback_fn(const char *message, void *data);
  *   - void secp256k1_default_error_callback_fn(const char *message, void *data);
- *  The library can call these default handlers even before a proper callback data
+ *  The library may call a default callback even before a proper callback data
  *  pointer could have been set using secp256k1_context_set_illegal_callback or
  *  secp256k1_context_set_error_callback, e.g., when the creation of a context
- *  fails. In this case, the corresponding default handler will be called with
+ *  fails. In this case, the corresponding default callback will be called with
  *  the data pointer argument set to NULL.
  *
  *  Args: ctx:  pointer to a context object.
  *  In:   fun:  pointer to a function to call when an illegal argument is
  *              passed to the API, taking a message and an opaque pointer.
- *              (NULL restores the default handler.)
- *        data: the opaque pointer to pass to fun above, must be NULL for the default handler.
+ *              (NULL restores the default callback.)
+ *        data: the opaque pointer to pass to fun above, must be NULL for the
+ *              default callback.
  *
  *  See also secp256k1_context_set_error_callback.
  */
@@ -380,8 +381,8 @@ SECP256K1_API void secp256k1_context_set_illegal_callback(
  *  to abort the program.
  *
  *  This can only trigger in case of a hardware failure, miscompilation,
- *  memory corruption, serious bug in the library, or other error would can
- *  otherwise result in undefined behaviour. It will not trigger due to mere
+ *  memory corruption, serious bug in the library, or other error that would
+ *  result in undefined behaviour. It will not trigger due to mere
  *  incorrect usage of the API (see secp256k1_context_set_illegal_callback
  *  for that). After this callback returns, anything may happen, including
  *  crashing.
@@ -389,9 +390,10 @@ SECP256K1_API void secp256k1_context_set_illegal_callback(
  *  Args: ctx:  pointer to a context object.
  *  In:   fun:  pointer to a function to call when an internal error occurs,
  *              taking a message and an opaque pointer (NULL restores the
- *              default handler, see secp256k1_context_set_illegal_callback
+ *              default callback, see secp256k1_context_set_illegal_callback
  *              for details).
- *        data: the opaque pointer to pass to fun above, must be NULL for the default handler.
+ *        data: the opaque pointer to pass to fun above, must be NULL for the
+ *              default callback.
  *
  *  See also secp256k1_context_set_illegal_callback.
  */