diff --git a/source/iterators.tex b/source/iterators.tex
index 6cb29652b1..a280be411f 100644
--- a/source/iterators.tex
+++ b/source/iterators.tex
@@ -1282,7 +1282,7 @@
 \begin{codeblock}
 template<class I>
   concept WeaklyIncrementable =
-    Semiregular<I> &&
+    DefaultConstructible<I> && Movable<I> &&
     requires(I i) {
       typename iter_difference_t<I>;
       requires SignedIntegral<iter_difference_t<I>>;
@@ -1379,6 +1379,12 @@
     WeaklyIncrementable<I>;
 \end{codeblock}
 
+\pnum
+\begin{note}
+Unlike the \oldconcept{Iterator} requirements,
+the \libconcept{Iterator} concept does not require copyability.
+\end{note}
+
 \rSec3[iterator.concept.sentinel]{Concept \tcode{Sentinel}}
 
 \pnum
@@ -1548,7 +1554,8 @@
 \rSec3[iterator.concept.forward]{Concept \tcode{ForwardIterator}}
 
 \pnum
-The \libconcept{ForwardIterator} concept adds equality comparison and
+The \libconcept{ForwardIterator} concept adds
+copyability, equality comparison, and
 the multi-pass guarantee, specified below.
 
 \indexlibrary{\idxcode{ForwardIterator}}%
@@ -3946,7 +3953,8 @@
     template<class U> constexpr move_iterator(const move_iterator<U>& u);
     template<class U> constexpr move_iterator& operator=(const move_iterator<U>& u);
 
-    constexpr iterator_type base() const;
+    constexpr iterator_type base() const &;
+    constexpr iterator_type base() &&;
     constexpr reference operator*() const;
 
     constexpr move_iterator& operator++();
@@ -4035,7 +4043,7 @@
 \begin{itemdescr}
 \pnum
 \effects Constructs a \tcode{move_iterator}, initializing
-\tcode{current} with \tcode{i}.
+\tcode{current} with \tcode{std::move(i)}.
 \end{itemdescr}
 
 
@@ -4071,14 +4079,30 @@
 
 \indexlibrarymember{base}{move_iterator}%
 \begin{itemdecl}
-constexpr Iterator base() const;
+constexpr Iterator base() const &;
 \end{itemdecl}
 
 \begin{itemdescr}
+\pnum
+\constraints \tcode{Iterator} satisfies \libconcept{CopyConstructible}.
+
+\pnum
+\expects \tcode{Iterator} models \libconcept{CopyConstructible}.
+
 \pnum
 \returns \tcode{current}.
 \end{itemdescr}
 
+\indexlibrarymember{base}{move_iterator}%
+\begin{itemdecl}
+constexpr Iterator base() &&;
+\end{itemdecl}
+
+\begin{itemdescr}
+\pnum
+\returns \tcode{std::move(current)}.
+\end{itemdescr}
+
 \rSec3[move.iter.elem]{Element access}
 
 \indexlibrarymember{operator*}{move_iterator}%
@@ -4944,7 +4968,8 @@
       requires Assignable<I&, const I2&>
         constexpr counted_iterator& operator=(const counted_iterator<I2>& x);
 
-    constexpr I base() const;
+    constexpr I base() const & requires CopyConstructible<I>;
+    constexpr I base() &&;
     constexpr iter_difference_t<I> count() const noexcept;
     constexpr decltype(auto) operator*();
     constexpr decltype(auto) operator*() const
@@ -5068,7 +5093,7 @@
 
 \indexlibrarymember{base}{counted_iterator}%
 \begin{itemdecl}
-constexpr I base() const;
+constexpr I base() const & requires CopyConstructible<I>;
 \end{itemdecl}
 
 \begin{itemdescr}
@@ -5076,6 +5101,16 @@
 \effects Equivalent to: \tcode{return current;}
 \end{itemdescr}
 
+\indexlibrarymember{base}{counted_iterator}%
+\begin{itemdecl}
+constexpr I base() &&;
+\end{itemdecl}
+
+\begin{itemdescr}
+\pnum
+\returns \tcode{std::move(current)}.
+\end{itemdescr}
+
 \indexlibrarymember{count}{counted_iterator}%
 \begin{itemdecl}
 constexpr iter_difference_t<I> count() const noexcept;