diff --git a/SRC/cgetsls.f b/SRC/cgetsls.f
index b4bb7562fc..10ecc70a73 100644
--- a/SRC/cgetsls.f
+++ b/SRC/cgetsls.f
@@ -22,8 +22,17 @@
 *>
 *> CGETSLS solves overdetermined or underdetermined complex linear systems
 *> involving an M-by-N matrix A, using a tall skinny QR or short wide LQ
-*> factorization of A.  It is assumed that A has full rank.
+*> factorization of A.
 *>
+*> It is assumed that A has full rank, and only a rudimentary protection
+*> against rank-deficient matrices is provided. This subroutine only detects
+*> exact rank-deficiency, where a diagonal element of the triangular factor
+*> of A is exactly zero.
+*>
+*> It is conceivable for one (or more) of the diagonal elements of the triangular
+*> factor of A to be subnormally tiny numbers without this subroutine signalling
+*> an error. The solutions computed for such almost-rank-deficient matrices may
+*> be less accurate due to a loss of numerical precision.
 *>
 *>
 *> The following options are provided:
@@ -141,7 +150,7 @@
 *>          = 0:  successful exit
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
 *>          > 0:  if INFO =  i, the i-th diagonal element of the
-*>                triangular factor of A is zero, so that A does not have
+*>                triangular factor of A is exactly zero, so that A does not have
 *>                full rank; the least squares solution could not be
 *>                computed.
 *> \endverbatim
diff --git a/SRC/dgetsls.f b/SRC/dgetsls.f
index 8d027f2c7d..add301761a 100644
--- a/SRC/dgetsls.f
+++ b/SRC/dgetsls.f
@@ -22,8 +22,17 @@
 *>
 *> DGETSLS solves overdetermined or underdetermined real linear systems
 *> involving an M-by-N matrix A, using a tall skinny QR or short wide LQ
-*> factorization of A.  It is assumed that A has full rank.
+*> factorization of A.
 *>
+*> It is assumed that A has full rank, and only a rudimentary protection
+*> against rank-deficient matrices is provided. This subroutine only detects
+*> exact rank-deficiency, where a diagonal element of the triangular factor
+*> of A is exactly zero.
+*>
+*> It is conceivable for one (or more) of the diagonal elements of the triangular
+*> factor of A to be subnormally tiny numbers without this subroutine signalling
+*> an error. The solutions computed for such almost-rank-deficient matrices may
+*> be less accurate due to a loss of numerical precision.
 *>
 *>
 *> The following options are provided:
@@ -141,7 +150,7 @@
 *>          = 0:  successful exit
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
 *>          > 0:  if INFO =  i, the i-th diagonal element of the
-*>                triangular factor of A is zero, so that A does not have
+*>                triangular factor of A is exactly zero, so that A does not have
 *>                full rank; the least squares solution could not be
 *>                computed.
 *> \endverbatim
diff --git a/SRC/sgetsls.f b/SRC/sgetsls.f
index d89c6a4e6d..e168723024 100644
--- a/SRC/sgetsls.f
+++ b/SRC/sgetsls.f
@@ -22,8 +22,17 @@
 *>
 *> SGETSLS solves overdetermined or underdetermined real linear systems
 *> involving an M-by-N matrix A, using a tall skinny QR or short wide LQ
-*> factorization of A.  It is assumed that A has full rank.
+*> factorization of A.
 *>
+*> It is assumed that A has full rank, and only a rudimentary protection
+*> against rank-deficient matrices is provided. This subroutine only detects
+*> exact rank-deficiency, where a diagonal element of the triangular factor
+*> of A is exactly zero.
+*>
+*> It is conceivable for one (or more) of the diagonal elements of the triangular
+*> factor of A to be subnormally tiny numbers without this subroutine signalling
+*> an error. The solutions computed for such almost-rank-deficient matrices may
+*> be less accurate due to a loss of numerical precision.
 *>
 *>
 *> The following options are provided:
@@ -141,7 +150,7 @@
 *>          = 0:  successful exit
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
 *>          > 0:  if INFO =  i, the i-th diagonal element of the
-*>                triangular factor of A is zero, so that A does not have
+*>                triangular factor of A is exactly zero, so that A does not have
 *>                full rank; the least squares solution could not be
 *>                computed.
 *> \endverbatim
diff --git a/SRC/zgetsls.f b/SRC/zgetsls.f
index b9adbc8325..d863876be9 100644
--- a/SRC/zgetsls.f
+++ b/SRC/zgetsls.f
@@ -22,8 +22,17 @@
 *>
 *> ZGETSLS solves overdetermined or underdetermined complex linear systems
 *> involving an M-by-N matrix A, using a tall skinny QR or short wide LQ
-*> factorization of A.  It is assumed that A has full rank.
+*> factorization of A.
 *>
+*> It is assumed that A has full rank, and only a rudimentary protection
+*> against rank-deficient matrices is provided. This subroutine only detects
+*> exact rank-deficiency, where a diagonal element of the triangular factor
+*> of A is exactly zero.
+*>
+*> It is conceivable for one (or more) of the diagonal elements of the triangular
+*> factor of A to be subnormally tiny numbers without this subroutine signalling
+*> an error. The solutions computed for such almost-rank-deficient matrices may
+*> be less accurate due to a loss of numerical precision.
 *>
 *>
 *> The following options are provided:
@@ -141,7 +150,7 @@
 *>          = 0:  successful exit
 *>          < 0:  if INFO = -i, the i-th argument had an illegal value
 *>          > 0:  if INFO =  i, the i-th diagonal element of the
-*>                triangular factor of A is zero, so that A does not have
+*>                triangular factor of A is exactly zero, so that A does not have
 *>                full rank; the least squares solution could not be
 *>                computed.
 *> \endverbatim