diff --git a/gtsam/inference/Permutation.h b/gtsam/inference/Permutation.h
index 985cc192f..8139bdd28 100644
--- a/gtsam/inference/Permutation.h
+++ b/gtsam/inference/Permutation.h
@@ -38,8 +38,19 @@ namespace gtsam {
  * that linearized factor graphs are already correctly ordered and need
  * not be permuted.
  *
- * Permutations can be considered to a 1-1 mapping from an original set of indices
- * to a different set of indices.  Permutations can be composed and inverted
+ * Consistent with their mathematical definition, permutations are functions
+ * that accept the destination index and return the source index.  For example,
+ * to permute data structure A into a new data structure B using permutation P,
+ * the mapping is B[i] = A[P[i]].  This is the behavior implemented by
+ * B = A.permute(P).
+ *
+ * For some data structures in GTSAM, for efficiency it is necessary to have
+ * the inverse of the desired permutation.  In this case, the data structure
+ * will implement permuteWithInverse(P) instead of permute(P).  You may already
+ * have the inverse permutation by construction, or may instead compute it with
+ * Pinv = P.inverse().
+ *
+ * Permutations can be composed and inverted
  * in order to create new indexing for a structure.
  * \nosubgrouping
  */
@@ -83,28 +94,28 @@ public:
   /// @{
 
   /**
-   * Return the new index of the supplied variable after the permutation
+   * Return the source index of the supplied destination index.
    */
   Index operator[](Index variable) const { check(variable); return rangeIndices_[variable]; }
 
   /**
-   * Return the new index of the supplied variable after the permutation. This version allows modification.
+   * Return the source index of the supplied destination index. This version allows modification.
    */
   Index& operator[](Index variable) { check(variable); return rangeIndices_[variable]; }
 
   /**
-   * Return the new index of the supplied variable after the permutation. Synonym for operator[](Index).
+   * Return the source index of the supplied destination index. Synonym for operator[](Index).
    */
   Index at(Index variable) const { return operator[](variable); }
 
   /**
-   * Return the new index of the supplied variable after the permutation. This version allows modification.   Synonym for operator[](Index).
+   * Return the source index of the supplied destination index. This version allows modification.   Synonym for operator[](Index).
    */
   Index& at(Index variable) { return operator[](variable); }
 
   /**
-   * The number of variables in the range of this permutation, i.e. the output
-   * space.
+   * The number of variables in the range of this permutation, i.e. the
+   * destination space.
    */
   Index size() const { return rangeIndices_.size(); }
 
@@ -143,8 +154,8 @@ public:
 
   /**
    * Return the inverse permutation.  This is only possible if this is a non-
-   * reducing permutation, that is, (*this)[i] < this->size() for all i<size().
-   * If NDEBUG is not defined, this conditional will be checked.
+   * reducing permutation, that is, (*this)[i] < this->size() for all
+   * i < size().  If NDEBUG is not defined, this conditional will be checked.
    */
   Permutation::shared_ptr inverse() const;