diff --git a/source/numerics.tex b/source/numerics.tex
index 31a2e217d6..5858279565 100644
--- a/source/numerics.tex
+++ b/source/numerics.tex
@@ -1558,62 +1558,56 @@
 
 \pnum
 Throughout \ref{rand},
-the effect of instantiating a template:
+where the template parameters are not constrained,
+the names of template parameters are used to express type requirements
+on an instantiated template $T$:
 \begin{itemize}
   \item
-    that has a template type parameter
+    If \tcode{T} has a template type parameter named
+    \tcode{Sseq}, \tcode{URBG}, \tcode{Engine},
+    \tcode{RealType}, \tcode{IntType}, or \tcode{UIntType},
+    the program is ill-formed if the corresponding template argument is cv-qualified.
+  \item
+    A template argument corresponding to a template parameter
     named \tcode{Sseq}
-    is undefined unless the corresponding template argument
-    is cv-unqualified and
-    meets the requirements
+    shall meet the requirements
     of seed sequence\iref{rand.req.seedseq}.
   \item
-    that has a template type parameter
+    A template argument corresponding to a template parameter
     named \tcode{URBG}
-    is undefined unless the corresponding template argument
-    is cv-unqualified and
-    meets the requirements
+    shall meet the requirements
     of uniform random bit generator\iref{rand.req.urng}.
   \item
-    that has a template type parameter
+    A template argument corresponding to a template parameter
     named \tcode{Engine}
-    is undefined unless the corresponding template argument
-    is cv-unqualified and
-    meets the requirements
+    shall meet the requirements
     of random number engine\iref{rand.req.eng}.
   \item
-    that has a template type parameter
+    If a template argument corresponding to a template parameter
     named \tcode{RealType}
-    is undefined unless the corresponding template argument
-    is cv-unqualified and
-    is one of
-    \tcode{float}, \tcode{double}, or \tcode{long double}.
+    is neither
+    a standard floating-point type ([basic.fundamental]) nor
+    a member of an implementation-defined subset of extended floating-point types,
+    the program is ill-formed.
   \item
-    that has a template type parameter
+    If a template argument corresponding to a template parameter
     named \tcode{IntType}
-    is undefined unless the corresponding template argument
-    is cv-unqualified and
-    is one of
-      \tcode{short},
-      \tcode{int},
-      \tcode{long},
-      \tcode{long long},
-      \tcode{unsigned short},
-      \tcode{unsigned int},
-      \tcode{unsigned long},
-      or
-      \tcode{unsigned long long}.
+    is neither
+    a standard signed nor a standard unsigned integer type\iref{basic.fundamental}, nor
+    an extended integer type whose width is
+    greater or equal to that of \tcode{char} and
+    less than or equal to that of \tcode{long long}, nor
+    a member of an implementation-defined subset of integer types,
+    the program is ill-formed.
   \item
-    that has a template type parameter
+    If a template argument corresponding to a template parameter
     named \tcode{UIntType}
-    is undefined unless the corresponding template argument
-    is cv-unqualified and
-    is one of
-      \tcode{unsigned short},
-      \tcode{unsigned int},
-      \tcode{unsigned long},
-      or
-      \tcode{unsigned long long}.
+    is neither
+    a standard or extended unsigned integer type whose width is
+    greater or equal to that of \tcode{short} and
+    less than or equal to that of \tcode{long long}, nor
+    a member of an implementation-defined subset of unsigned integer types,
+    the program is ill-formed.
 \end{itemize}
 
 \pnum