diff --git a/source/iterators.tex b/source/iterators.tex
index f38f819f83..cb60f0a9be 100644
--- a/source/iterators.tex
+++ b/source/iterators.tex
@@ -384,10 +384,8 @@
   // \ref{iterators.counted}, counted iterators
   template<@\libconcept{input_or_output_iterator}@ I> class counted_iterator;
 
-  template<class I>
-    struct incrementable_traits<counted_iterator<I>>;
-
   template<@\libconcept{input_iterator}@ I>
+    requires @\seebelow@
     struct iterator_traits<counted_iterator<I>>;
 
   // \ref{unreachable.sentinel}, unreachable sentinel
@@ -1011,6 +1009,14 @@
 Explicit or partial specializations of \tcode{iterator_traits} may
 have a member type \tcode{iterator_concept} that is used to indicate
 conformance to the iterator concepts\iref{iterator.concepts}.
+\begin{example}
+To indicate conformance to the \libconcept{input_iterator} concept
+but a lack of conformance to
+the \oldconcept{InputIter\-ator} requirements\iref{input.iterators},
+an \tcode{iterator_traits} specialization might have
+\tcode{iterator_concept} denote \tcode{input_iterator_tag}
+but not define \tcode{iterator_category}.
+\end{example}
 
 \pnum
 \tcode{iterator_traits} is specialized for pointers as
@@ -4085,7 +4091,7 @@
   public:
     using iterator_type     = Iterator;
     using iterator_concept  = input_iterator_tag;
-    using iterator_category = @\seebelow@;
+    using iterator_category = @\seebelow@;                      // not always present
     using value_type        = iter_value_t<Iterator>;
     using difference_type   = iter_difference_t<Iterator>;
     using pointer           = Iterator;
@@ -4135,7 +4141,11 @@
 \end{codeblock}
 
 \pnum
-The member \grammarterm{typedef-name} \tcode{iterator_category} denotes
+The member \grammarterm{typedef-name} \tcode{iterator_category} is defined
+if and only if the \grammarterm{qualified-id}
+\tcode{iterator_traits<It\-erator>::iterator_category}
+is valid and denotes a type.
+In that case, \tcode{iterator_category} denotes
 \begin{itemize}
 \item
 \tcode{random_access_iterator_tag} if
@@ -4795,7 +4805,8 @@
 \item
 \tcode{iterator_category} denotes
 \tcode{forward_iterator_tag}
-if \tcode{iterator_traits<I>::iterator_category}
+if the \grammarterm{qualified-id} \tcode{iterator_traits<I>::iter\-ator_category}
+is valid and denotes a type that
 models \tcode{\libconcept{derived_from}<forward_iterator_tag>};
 otherwise it denotes \tcode{input_iterator_tag}.
 
@@ -4990,7 +5001,33 @@
 ++*this;
 return tmp;
 \end{codeblock}
-Otherwise, equivalent to: \tcode{return get<I>(v_)++;}
+Otherwise, if
+\tcode{requires (I\& i) \{ \{ *i++ \} -> \exposconceptnc{can-reference}; \}}
+is \tcode{true} or
+\tcode{\libconcept{constructible_\newline{}from}<iter_value_t<I>, iter_reference_t<I>>}
+is \tcode{false},
+equivalent to:
+\begin{codeblock}
+return get<I>(v_)++;
+\end{codeblock}
+Otherwise, equivalent to:
+\begin{codeblock}
+@\exposid{postfix-proxy}@ p(**this);
+++*this;
+return p;
+\end{codeblock}
+where \exposid{postfix-proxy} is the exposition-only class:
+\begin{codeblock}
+class @\exposid{postfix-proxy}@ {
+  iter_value_t<I> keep_;
+  @\exposid{postfix-proxy}@(iter_reference_t<I>&& x)
+    : keep_(std::move(x)) {}
+public:
+  const iter_value_t<I>& operator*() const {
+    return keep_;
+  }
+};
+\end{codeblock}
 \end{itemdescr}
 
 \rSec3[common.iter.cmp]{Comparisons}
@@ -5151,7 +5188,13 @@
   class counted_iterator {
   public:
     using iterator_type = I;
-
+    using value_type = iter_value_t<I>;                         // present only
+                        // if \tcode{I} models \libconcept{indirectly_readable}
+    using difference_type = iter_difference_t<I>;
+    using iterator_concept = typename I::iterator_concept;      // present only
+                        // if the \grammarterm{qualified-id} \tcode{I::iterator_concept} is valid and denotes a type
+    using iterator_category = typename I::iterator_category;    // present only
+                        // if the \grammarterm{qualified-id} \tcode{I::iterator_category} is valid and denotes a type
     constexpr counted_iterator() = default;
     constexpr counted_iterator(I x, iter_difference_t<I> n);
     template<class I2>
@@ -5169,6 +5212,9 @@
     constexpr decltype(auto) operator*() const
       requires @\exposconcept{dereferenceable}@<const I>;
 
+    constexpr auto operator->() const noexcept
+      requires @\libconcept{contiguous_iterator}@<I>;
+
     constexpr counted_iterator& operator++();
     decltype(auto) operator++(int);
     constexpr counted_iterator operator++(int)
@@ -5223,14 +5269,11 @@
     iter_difference_t<I> length = 0;    // \expos
   };
 
-  template<class I>
-  struct incrementable_traits<counted_iterator<I>> {
-    using difference_type = iter_difference_t<I>;
-  };
-
   template<@\libconcept{input_iterator}@ I>
+    requires @\libconcept{same_as}@<@\exposid{ITER_TRAITS}@(I), iterator_traits<I>>   // see \ref{iterator.concepts.general}
   struct iterator_traits<counted_iterator<I>> : iterator_traits<I> {
-    using pointer = void;
+    using pointer = conditional_t<@\libconcept{contiguous_iterator}@<I>,
+                                  add_pointer_t<iter_reference_t<I>>, void>;
   };
 }
 \end{codeblock}
@@ -5339,6 +5382,18 @@
 Equivalent to: \tcode{return *current;}
 \end{itemdescr}
 
+\indexlibrarymember{operator->}{counted_iterator}%
+\begin{itemdecl}
+constexpr auto operator->() const noexcept
+  requires @\libconcept{contiguous_iterator}@<I>;
+\end{itemdecl}
+
+\begin{itemdescr}
+\pnum
+\effects
+Equivalent to: \tcode{return to_address(current);}
+\end{itemdescr}
+
 \indexlibrarymember{operator[]}{counted_iterator}%
 \begin{itemdecl}
 constexpr decltype(auto) operator[](iter_difference_t<I> n) const
diff --git a/source/ranges.tex b/source/ranges.tex
index 4477268a95..00fa442bea 100644
--- a/source/ranges.tex
+++ b/source/ranges.tex
@@ -2309,7 +2309,7 @@
     W @\exposid{value_}@ = W();             // \expos
   public:
     using iterator_concept = @\seebelow@;
-    using iterator_category = input_iterator_tag;
+    using iterator_category = input_iterator_tag;       // present only if \tcode{W} models \libconcept{incrementable}
     using value_type = W;
     using difference_type = @\placeholdernc{IOTA-DIFF-T}@(W);
 
@@ -3269,7 +3269,7 @@
     filter_view* @\exposid{parent_}@ = nullptr;             // \expos
   public:
     using iterator_concept  = @\seebelow@;
-    using iterator_category = @\seebelow@;
+    using iterator_category = @\seebelow@;        // not always present
     using value_type        = range_value_t<V>;
     using difference_type   = range_difference_t<V>;
 
@@ -3320,6 +3320,9 @@
 \end{itemize}
 
 \pnum
+The member \grammarterm{typedef-name} \tcode{iterator_category} is defined
+if and only if \tcode{V} models \libconcept{forward_range}.
+In that case,
 \tcode{\exposid{iterator}::iterator_category} is defined as follows:
 \begin{itemize}
 \item Let \tcode{C} denote the type
@@ -3759,7 +3762,7 @@
     @\exposid{Parent}@* @\exposid{parent_}@ = nullptr;                                  // \expos
   public:
     using iterator_concept  = @\seebelow@;
-    using iterator_category = @\seebelow@;
+    using iterator_category = @\seebelow@;                        // not always present
     using value_type        =
       remove_cvref_t<invoke_result_t<F&, range_reference_t<@\exposid{Base}@>>>;
     using difference_type   = range_difference_t<@\exposid{Base}@>;
@@ -3846,6 +3849,9 @@
 \end{itemize}
 
 \pnum
+The member \grammarterm{typedef-name} \tcode{iterator_category} is defined
+if and only if \exposid{Base} models \libconcept{forward_range}.
+In that case,
 \tcode{iterator::iterator_category} is defined as follows:
 Let \tcode{C} denote the type
 \tcode{iterator_traits<iterator_t<\exposid{Base}>>::iterator_category}.
@@ -5071,7 +5077,7 @@
     constexpr void @\exposid{satisfy}@();                                   // \expos
   public:
     using iterator_concept  = @\seebelow@;
-    using iterator_category = @\seebelow@;
+    using iterator_category = @\seebelow@;                        // not always present
     using value_type        = range_value_t<range_reference_t<@\exposid{Base}@>>;
     using difference_type   = @\seebelow@;
 
@@ -5133,24 +5139,27 @@
 \end{itemize}
 
 \pnum
-\tcode{iterator::iterator_category} is defined as follows:
+The member \grammarterm{typedef-name} \tcode{iterator_category} is defined
+if and only if \exposid{ref-is-glvalue} is \tcode{true},
+\exposid{Base} models \libconcept{forward_range}, and
+\tcode{range_reference_t<\exposid{Base}>} models \libconcept{forward_range}.
+In that case,
+\tcode{iterator::iter\-ator_category} is defined as follows:
 \begin{itemize}
 \item Let \placeholder{OUTERC} denote
   \tcode{iterator_traits<iterator_t<\exposid{Base}>>::iterator_category}, and
   let \placeholder{INNERC} denote
   \tcode{iterator_traits<iterator_t<range_reference_t<\exposid{Base}>>>::iterator_category}.
-\item If \exposid{ref-is-glvalue} is \tcode{true} and
+\item If
   \placeholder{OUTERC} and \placeholder{INNERC} each model
   \tcode{\libconcept{derived_from}<bidirectional_iterator_tag>}, \tcode{iterator_category}
   denotes \tcode{bidirectional_iterator_tag}.
-\item Otherwise, if \exposid{ref-is-glvalue} is \tcode{true} and
+\item Otherwise, if
   \placeholder{OUTERC} and \placeholder{INNERC} each model
-  \tcode{\libconcept{derived_from}<for\-ward_iterator_tag>}, \tcode{iterator_category}
+  \tcode{\libconcept{derived_from}<forward_iterator_tag>}, \tcode{iter\-ator_category}
   denotes \tcode{forward_iterator_tag}.
-\item Otherwise, if \placeholder{OUTERC} and \placeholder{INNERC} each model
-  \tcode{\libconcept{derived_from}<input_iterator_tag>},
+\item Otherwise,
   \tcode{iterator_category} denotes \tcode{input_iterator_tag}.
-\item Otherwise, \tcode{iterator_category} denotes \tcode{output_iterator_tag}.
 \end{itemize}
 
 \pnum
@@ -5572,7 +5581,7 @@
   public:
     using iterator_concept  =
       conditional_t<@\libconcept{forward_range}@<@\exposid{Base}@>, forward_iterator_tag, input_iterator_tag>;
-    using iterator_category = input_iterator_tag;
+    using iterator_category = input_iterator_tag;       // present only if \exposid{Base} models \libconcept{forward_range}
     // \ref{range.split.outer.value}, class \tcode{split_view::\exposid{outer-iterator}::value_type}
     struct value_type;
     using difference_type   = range_difference_t<@\exposid{Base}@>;
@@ -5801,7 +5810,7 @@
     bool @\exposid{incremented_}@ = false;                          // \expos
   public:
     using iterator_concept  = typename @\exposid{outer-iterator}@<Const>::iterator_concept;
-    using iterator_category = @\seebelow@;
+    using iterator_category = @\seebelow@;              // present only if \exposid{Base} models \libconcept{forward_range}
     using value_type        = range_value_t<@\exposid{Base}@>;
     using difference_type   = range_difference_t<@\exposid{Base}@>;
 
@@ -6395,7 +6404,8 @@
     static constexpr decltype(auto) @\exposid{get-element}@(const iterator_t<@\exposid{Base}@>& i);     // \expos
 
   public:
-    using iterator_category = typename iterator_traits<iterator_t<@\exposid{Base}@>>::iterator_category;
+    using iterator_concept = @\seebelow@;
+    using iterator_category = @\seebelow@;                // not always present
     using value_type = remove_cvref_t<tuple_element_t<N, range_value_t<@\exposid{Base}@>>>;
     using difference_type = range_difference_t<@\exposid{Base}@>;
 
@@ -6453,6 +6463,40 @@
 }
 \end{codeblock}
 
+\pnum
+The member \grammarterm{typedef-name} \tcode{iterator_concept}
+is defined as follows:
+\begin{itemize}
+\item
+If \tcode{V} models \libconcept{random_access_range},
+then \tcode{iterator_concept} denotes \tcode{random_access_iterator_tag}.
+\item
+Otherwise, if \tcode{V} models \libconcept{bidirectional_range},
+then \tcode{iterator_concept} denotes \tcode{bidirectional_iterator_tag}.
+\item
+Otherwise, if \tcode{V} models \libconcept{forward_range},
+then \tcode{iterator_concept} denotes \tcode{forward_iterator_tag}.
+\item
+Otherwise, \tcode{iterator_concept} denotes \tcode{input_iterator_tag}.
+\end{itemize}
+
+\pnum
+The member \grammarterm{typedef-name} \tcode{iterator_category} is defined
+if and only if \exposid{Base} models \libconcept{forward_range}.
+In that case, \tcode{iterator_category} is defined as follows:
+Let \tcode{C} denote the type
+\tcode{iterator_traits<iterator_t<\exposid{Base}>>::iterator_category}.
+\begin{itemize}
+\item
+If \tcode{get<N>(*\exposid{current_})} is an rvalue,
+\tcode{iterator_category} denotes \tcode{input_iterator_tag}.
+\item
+Otherwise, if \tcode{C} models \tcode{\libconcept{derived_from}<random_access_iterator_tag>},
+\tcode{iterator_category} denotes \tcode{random_access_iterator_tag}.
+\item
+Otherwise, \tcode{iterator_category} denotes \tcode{C}.
+\end{itemize}
+
 \indexlibrarymember{\exposid{get-element}}{elements_view::iterator}%
 \begin{itemdecl}
 static constexpr decltype(auto) @\exposid{get-element}@(const iterator_t<@\exposid{Base}@>& i);     // \expos