diff --git a/include/graphblas/descriptors.hpp b/include/graphblas/descriptors.hpp
index ea2331f6c..1fe3f9836 100644
--- a/include/graphblas/descriptors.hpp
+++ b/include/graphblas/descriptors.hpp
@@ -24,21 +24,31 @@
  * @date 15 March, 2016
  */
 
-#include <sstream>
-#include <string>
-
 #ifndef _H_GRB_DESCRIPTOR
 #define _H_GRB_DESCRIPTOR
 
+#include <string>
+
+
 namespace grb {
 
 	/**
 	 * Descriptors indicate pre- or post-processing for some or all of the
-	 * arguments to a GraphBLAS call.
+	 * arguments to an ALP/GraphBLAS call. An example is to transpose the input
+	 * matrix during a sparse matrix--vector multiplication:
+	 *    <tt>grb::mxv< grb::descriptors::transpose_matrix >( y, A, x, ring );</tt>
+	 * the above thus computes \f$ y \to y + A^Tx \f$ and not \f$ y \to y + Ax \f$.
+	 *
+	 * Such pre-processing often happens on-the-fly, without significant overhead
+	 * to the primitive costings in any of its cost dimensions -- work, intra- and
+	 * inter-process data movement, synchronisations, and memory usage.
 	 *
-	 * They can be combined using bit-wise operators. For instance, to both
-	 * indicate the matrix needs be transposed and the mask needs be
-	 * inverted, the following descriptor can be passed:
+	 * \note If the application of a descriptor is \em not without significant
+	 *       overhead, a backend \em must clearly indicate so.
+	 *
+	 * Descriptors may be combined using bit-wise operators. For instance, to both
+	 * indicate the matrix needs be transposed and the mask needs be inverted, the
+	 * following descriptor can be passed:
 	 *    <tt> transpose_matrix | invert_mask </tt>
 	 */
 	typedef unsigned int Descriptor;
@@ -107,9 +117,31 @@ namespace grb {
 		static constexpr Descriptor structural_complement = structural | invert_mask;
 
 		/**
-		 * Indicates all vectors used in a computation are dense. This is a hint that
-		 * might affect performance but will never affect the semantics of the
-		 * computation.
+		 * Indicates that all input vectors to an ALP/GraphBLAS primitive are
+		 * structurally dense.
+		 *
+		 * If a user passes this descriptor but one or more vectors input to the call
+		 * are \em not structurally dense, then #ILLEGAL shall be returned.
+		 *
+		 * \warning <em>All vectors</em> includes any vectors that operate as masks.
+		 *          Thus if the primitive is to operate with structurally sparse masks
+		 *          but with otherwise dense vectors, then the dense descriptor may
+		 *          \em not be defined.
+		 *
+		 * \warning For in-place operations with vector outputs --which are all
+		 *          ALP/GraphBLAS primitives with vector outputs except grb::set and
+		 *          grb::eWiseApply-- the output vector is also an input vector. Thus
+		 *          passing this descriptor to such primitive indicates that also the
+		 *          output vector is structurally dense.
+		 *
+		 * \warning Vectors with explicit zeroes (under the semiring passed to the
+		 *          related primitive) will be computed with explicitly.
+		 *
+		 * The benefits of using this descriptor whenever possible are two-fold:
+		 *   1) less run-time overhead as code handling sparsity is disabled;
+		 *   2) smaller binary sizes as code handling structurally sparse vectors is
+		 *      not emitted (unless required elsewhere).
+		 * The consistent use of this descriptor is hence strongly encouraged.
 		 */
 		static constexpr Descriptor dense = 16;
 
diff --git a/src/graphblas/descriptors.cpp b/src/graphblas/descriptors.cpp
index 0dfcf29b3..60e5db4f9 100644
--- a/src/graphblas/descriptors.cpp
+++ b/src/graphblas/descriptors.cpp
@@ -17,6 +17,9 @@
 
 #include <graphblas/descriptors.hpp>
 
+#include <sstream>
+
+
 std::string grb::descriptors::toString( const grb::Descriptor descr ) {
 	std::ostringstream os;
 	if( descr == 0 ) {
@@ -36,23 +39,22 @@ std::string grb::descriptors::toString( const grb::Descriptor descr ) {
 			os << " mask must be interpreted structurally, and not by value\n";
 		}
 		if( descr & dense ) {
-			os << " user guarantees all vectors in this call are dense\n";
+			os << " user guarantees that all input vectors to this call are dense\n";
 		}
 		if( descr & add_identity ) {
 			os << " an identity matrix is added to the input matrix\n";
 		}
 		if( descr & use_index ) {
-			os << " instead of using input vector elements, use their index "
-				  "instead\n";
+			os << " instead of using input vector elements, use their index instead\n";
 		}
 		if( descr & explicit_zero ) {
 			os << " the operation should take zeroes into account explicitly "
 				  "when computing output\n";
 		}
 		if( descr & no_casting ) {
-			os << " disallow casting between types during the requested "
-				  "computation\n";
+			os << " disallow casting between types during the requested computation\n";
 		}
 	}
 	return os.str();
 }
+