diff --git a/doc/concepts/Axis.qbk b/doc/concepts/Axis.qbk
index 44fc7ca9..9fc866df 100644
--- a/doc/concepts/Axis.qbk
+++ b/doc/concepts/Axis.qbk
@@ -51,7 +51,7 @@ An [*Axis] maps input values to indices. It holds state specific to that axis, l
 * `a` and `b` are values of type `A`
 * `i` and `j` are indices of type [headerref boost/histogram/fwd.hpp `boost::histogram::axis::index_type`]
 * `n` is a value of type `unsigned`
-* `M` is a metadata type that is [@https://en.cppreference.com/w/cpp/named_req/CopyConstructible CopyConstructible] and [@https://en.cppreference.com/w/cpp/named_req/CopyAssignable CopyAssignable] and *nothrow* [@https://en.cppreference.com/w/cpp/named_req/MoveAssignable MoveAssignable].
+* `M` is a metadata type that is [@https://en.cppreference.com/w/cpp/named_req/DefaultConstructible DefaultConstructible], [@https://en.cppreference.com/w/cpp/named_req/CopyConstructible CopyConstructible] and [@https://en.cppreference.com/w/cpp/named_req/CopyAssignable CopyAssignable]. It it supports moves, it must be *nothrow* [@https://en.cppreference.com/w/cpp/named_req/MoveAssignable MoveAssignable].
 * `ar` is a value of an archive with Boost.Serialization semantics
 
 [table Valid expressions
diff --git a/include/boost/histogram/axis/boolean.hpp b/include/boost/histogram/axis/boolean.hpp
index 0549b70b..5fd0879a 100644
--- a/include/boost/histogram/axis/boolean.hpp
+++ b/include/boost/histogram/axis/boolean.hpp
@@ -39,10 +39,14 @@ class boolean : public iterator_mixin<boolean<MetaData>>,
 
 public:
   /** Construct a boolean axis.
-   *
-   * @param meta description of the axis.
+
+    @param meta description of the axis.
+
+    The constructor is nothrow if meta is nothrow move constructible.
    */
-  explicit boolean(metadata_type meta = {}) : metadata_base(std::move(meta)) {}
+  explicit boolean(metadata_type meta = {}) noexcept(
+      std::is_nothrow_move_constructible<metadata_type>::value)
+      : metadata_base(std::move(meta)) {}
 
   /// Return index for value argument.
   index_type index(value_type x) const noexcept { return static_cast<index_type>(x); }
diff --git a/include/boost/histogram/axis/category.hpp b/include/boost/histogram/axis/category.hpp
index 0c705afb..9802c95d 100644
--- a/include/boost/histogram/axis/category.hpp
+++ b/include/boost/histogram/axis/category.hpp
@@ -28,18 +28,18 @@ namespace axis {
 
 /** Maps at a set of unique values to bin indices.
 
-   The axis maps a set of values to bins, following the order of arguments in the
-   constructor. The optional overflow bin for this axis counts input values that
-   are not part of the set. Binning has O(N) complexity, but with a very small
-   factor. For small N (the typical use case) it beats other kinds of lookup.
-
-   @tparam Value input value type, must be equal-comparable.
-   @tparam MetaData type to store meta data.
-   @tparam Options see boost::histogram::axis::option.
-   @tparam Allocator allocator to use for dynamic memory management.
-
-   The options `underflow` and `circular` are not allowed. The options `growth`
-   and `overflow` are mutually exclusive.
+  The axis maps a set of values to bins, following the order of arguments in the
+  constructor. The optional overflow bin for this axis counts input values that
+  are not part of the set. Binning has O(N) complexity, but with a very small
+  factor. For small N (the typical use case) it beats other kinds of lookup.
+
+  @tparam Value input value type, must be equal-comparable.
+  @tparam MetaData type to store meta data.
+  @tparam Options see boost::histogram::axis::option.
+  @tparam Allocator allocator to use for dynamic memory management.
+
+  The options `underflow` and `circular` are not allowed. The options `growth`
+  and `overflow` are mutually exclusive.
  */
 template <class Value, class MetaData, class Options, class Allocator>
 class category : public iterator_mixin<category<Value, MetaData, Options, Allocator>>,
@@ -56,13 +56,20 @@ class category : public iterator_mixin<category<Value, MetaData, Options, Alloca
   constexpr category() = default;
   explicit category(allocator_type alloc) : vec_(alloc) {}
 
-  /** Construct from iterator range of unique values.
+  /** Construct from forward iterator range of unique values.
 
-     @param begin    begin of category range of unique values.
-     @param end      end of category range of unique values.
-     @param meta     description of the axis (optional).
-     @param options  see boost::histogram::axis::option (optional).
-     @param alloc    allocator instance to use (optional).
+    @param begin    begin of category range of unique values.
+    @param end      end of category range of unique values.
+    @param meta     description of the axis (optional).
+    @param options  see boost::histogram::axis::option (optional).
+    @param alloc    allocator instance to use (optional).
+
+    The constructor throws `std::invalid_argument` if iterator range is invalid. If the
+    range contains duplicated values, the behavior of the axis is undefined.
+
+    The arguments meta and alloc are passed by value. If you move either of them into the
+    axis and the constructor throws, their values are lost. Do not move if you cannot
+    guarantee that the bin description is not valid.
    */
   template <class It, class = detail::requires_iterator<It>>
   category(It begin, It end, metadata_type meta = {}, options_type options = {},
diff --git a/include/boost/histogram/axis/integer.hpp b/include/boost/histogram/axis/integer.hpp
index d61dfdd8..a40ac5ff 100644
--- a/include/boost/histogram/axis/integer.hpp
+++ b/include/boost/histogram/axis/integer.hpp
@@ -31,11 +31,13 @@ namespace axis {
 
 /** Axis for an interval of integer values with unit steps.
 
-   Binning is a O(1) operation. This axis bins faster than a regular axis.
+  Binning is a O(1) operation. This axis bins even faster than a regular axis.
 
-   @tparam Value     input value type. Must be integer or floating point.
-   @tparam MetaData  type to store meta data.
-   @tparam Options   see boost::histogram::axis::option.
+  The options `growth` and `circular` are mutually exclusive.
+
+  @tparam Value     input value type. Must be integer or floating point.
+  @tparam MetaData  type to store meta data.
+  @tparam Options   see boost::histogram::axis::option.
  */
 template <class Value, class MetaData, class Options>
 class integer : public iterator_mixin<integer<Value, MetaData, Options>>,
@@ -47,23 +49,6 @@ class integer : public iterator_mixin<integer<Value, MetaData, Options>>,
   using options_type =
       detail::replace_default<Options, decltype(option::underflow | option::overflow)>;
 
-  static_assert(std::is_integral<value_type>::value ||
-                    std::is_floating_point<value_type>::value,
-                "integer axis requires floating point or integral type");
-
-  static_assert(!options_type::test(option::circular | option::growth) ||
-                    (options_type::test(option::circular) ^
-                     options_type::test(option::growth)),
-                "circular and growth options are mutually exclusive");
-
-  static_assert(std::is_floating_point<value_type>::value ||
-                    (!options_type::test(option::circular) &&
-                     !options_type::test(option::growth)) ||
-                    (!options_type::test(option::overflow) &&
-                     !options_type::test(option::underflow)),
-                "circular or growing integer axis with integral type "
-                "cannot have entries in underflow or overflow bins");
-
   using local_index_type = std::conditional_t<std::is_integral<value_type>::value,
                                               index_type, real_index_type>;
 
@@ -72,18 +57,37 @@ class integer : public iterator_mixin<integer<Value, MetaData, Options>>,
 
   /** Construct over semi-open integer interval [start, stop).
 
-     @param start    first integer of covered range.
-     @param stop     one past last integer of covered range.
-     @param meta     description of the axis (optional).
-     @param options  see boost::histogram::axis::option (optional).
+    @param start    first integer of covered range.
+    @param stop     one past last integer of covered range.
+    @param meta     description of the axis (optional).
+    @param options  see boost::histogram::axis::option (optional).
+
+    The constructor throws `std::invalid_argument` if start is not less than stop.
+
+    The arguments meta and alloc are passed by value. If you move either of them into the
+    axis and the constructor throws, their values are lost. Do not move if you cannot
+    guarantee that the bin description is not valid.
    */
   integer(value_type start, value_type stop, metadata_type meta = {},
           options_type options = {})
       : metadata_base(std::move(meta))
       , size_(static_cast<index_type>(stop - start))
       , min_(start) {
-    (void)options;
-    if (!(stop >= start))
+    static_assert(
+        std::is_integral<value_type>::value || std::is_floating_point<value_type>::value,
+        "integer axis requires floating point or integral type");
+
+    static_assert(!(options.test(option::circular) && options.test(option::growth)),
+                  "circular and growth options are mutually exclusive");
+
+    static_assert(
+        std::is_floating_point<value_type>::value ||
+            !((options.test(option::growth) || options.test(option::circular)) &&
+              (options.test(option::overflow) || options.test(option::underflow))),
+        "circular or growing integer axis with integral type "
+        "cannot have entries in underflow or overflow bins");
+
+    if (!(stop >= start)) // double negation so it works with NaN
       BOOST_THROW_EXCEPTION(std::invalid_argument("stop >= start required"));
   }
 
diff --git a/include/boost/histogram/axis/metadata_base.hpp b/include/boost/histogram/axis/metadata_base.hpp
index 520d82c5..94da12d2 100644
--- a/include/boost/histogram/axis/metadata_base.hpp
+++ b/include/boost/histogram/axis/metadata_base.hpp
@@ -27,6 +27,15 @@ class metadata_base {
 protected:
   using metadata_type = Metadata;
 
+  static_assert(std::is_default_constructible<metadata_type>::value,
+                "metadata must be default constructible");
+
+  static_assert(std::is_copy_constructible<metadata_type>::value,
+                "metadata must be copy constructible");
+
+  static_assert(std::is_copy_assignable<metadata_type>::value,
+                "metadata must be copy assignable");
+
   // std::string explicitly guarantees nothrow only in C++17
   static_assert(std::is_same<metadata_type, std::string>::value ||
                     std::is_nothrow_move_constructible<metadata_type>::value,
@@ -45,15 +54,15 @@ class metadata_base {
     return *this;
   }
 
-private:
-  mutable metadata_type data_;
-
 public:
   /// Returns reference to metadata.
   metadata_type& metadata() noexcept { return data_; }
 
   /// Returns reference to mutable metadata from const axis.
   metadata_type& metadata() const noexcept { return data_; }
+
+private:
+  mutable metadata_type data_;
 };
 
 #ifndef BOOST_HISTOGRAM_DOXYGEN_INVOKED
diff --git a/include/boost/histogram/axis/regular.hpp b/include/boost/histogram/axis/regular.hpp
index 2fb5dee0..a5c7c124 100644
--- a/include/boost/histogram/axis/regular.hpp
+++ b/include/boost/histogram/axis/regular.hpp
@@ -167,20 +167,20 @@ step_type<T> step(T t) {
 
 /** Axis for equidistant intervals on the real line.
 
-   The most common binning strategy. Very fast. Binning is a O(1) operation.
+  The most common binning strategy. Very fast. Binning is a O(1) operation.
 
-   If the axis has an overflow bin (the default), a value on the upper edge of the last
-   bin is put in the overflow bin. The axis range represents a semi-open interval.
+  If the axis has an overflow bin (the default), a value on the upper edge of the last
+  bin is put in the overflow bin. The axis range represents a semi-open interval.
 
-   If the overflow bin is deactivated, then a value on the upper edge of the last bin is
-   still counted towards the last bin. The axis range represents a closed interval. This
-   is the desired behavior for random numbers drawn from a bounded interval, which is
-   usually closed.
+  If the overflow bin is deactivated, then a value on the upper edge of the last bin is
+  still counted towards the last bin. The axis range represents a closed interval.
 
-   @tparam Value input value type, must be floating point.
-   @tparam Transform builtin or user-defined transform type.
-   @tparam MetaData type to store meta data.
-   @tparam Options see boost::histogram::axis::option.
+  The options `growth` and `circular` are mutually exclusive.
+
+  @tparam Value input value type, must be floating point.
+  @tparam Transform builtin or user-defined transform type.
+  @tparam MetaData type to store meta data.
+  @tparam Options see boost::histogram::axis::option.
  */
 template <class Value, class Transform, class MetaData, class Options>
 class regular : public iterator_mixin<regular<Value, Transform, MetaData, Options>>,
@@ -202,12 +202,19 @@ class regular : public iterator_mixin<regular<Value, Transform, MetaData, Option
 
   /** Construct n bins over real transformed range [start, stop).
 
-     @param trans    transform instance to use.
-     @param n        number of bins.
-     @param start    low edge of first bin.
-     @param stop     high edge of last bin.
-     @param meta     description of the axis (optional).
-     @param options  see boost::histogram::axis::option (optional).
+    @param trans    transform instance to use.
+    @param n        number of bins.
+    @param start    low edge of first bin.
+    @param stop     high edge of last bin.
+    @param meta     description of the axis (optional).
+    @param options  see boost::histogram::axis::option (optional).
+
+    The constructor throws `std::invalid_argument` if n is zero, or if start and stop
+    produce an invalid range after transformation.
+
+    The arguments meta and alloc are passed by value. If you move either of them into the
+    axis and the constructor throws, their values are lost. Do not move if you cannot
+    guarantee that the bin description is not valid.
    */
   regular(transform_type trans, unsigned n, value_type start, value_type stop,
           metadata_type meta = {}, options_type options = {})
@@ -223,10 +230,9 @@ class regular : public iterator_mixin<regular<Value, Transform, MetaData, Option
                   "transform must be no-throw move assignable");
     static_assert(std::is_floating_point<internal_value_type>::value,
                   "regular axis requires floating point type");
-    static_assert((!options.test(option::circular) && !options.test(option::growth)) ||
-                      (options.test(option::circular) ^ options.test(option::growth)),
+    static_assert(!(options.test(option::circular) && options.test(option::growth)),
                   "circular and growth options are mutually exclusive");
-    if (size() == 0) BOOST_THROW_EXCEPTION(std::invalid_argument("bins > 0 required"));
+    if (size() <= 0) BOOST_THROW_EXCEPTION(std::invalid_argument("bins > 0 required"));
     if (!std::isfinite(min_) || !std::isfinite(delta_))
       BOOST_THROW_EXCEPTION(
           std::invalid_argument("forward transform of start or stop invalid"));
diff --git a/include/boost/histogram/axis/variable.hpp b/include/boost/histogram/axis/variable.hpp
index f866e098..6be785e7 100644
--- a/include/boost/histogram/axis/variable.hpp
+++ b/include/boost/histogram/axis/variable.hpp
@@ -68,13 +68,20 @@ class variable : public iterator_mixin<variable<Value, MetaData, Options, Alloca
   constexpr variable() = default;
   explicit variable(allocator_type alloc) : vec_(alloc) {}
 
-  /** Construct from iterator range of bin edges.
+  /** Construct from forward iterator range of bin edges.
 
-     @param begin   begin of edge sequence.
-     @param end     end of edge sequence.
-     @param meta    description of the axis (optional).
-     @param options see boost::histogram::axis::option (optional).
-     @param alloc   allocator instance to use (optional).
+    @param begin   begin of edge sequence.
+    @param end     end of edge sequence.
+    @param meta    description of the axis (optional).
+    @param options see boost::histogram::axis::option (optional).
+    @param alloc   allocator instance to use (optional).
+
+    The constructor throws `std::invalid_argument` if iterator range is invalid, if less
+    than two edges are provided or if bin edges are not in ascending order.
+
+    The arguments meta and alloc are passed by value. If you move either of them into the
+    axis and the constructor throws, their values are lost. Do not move if you cannot
+    guarantee that the bin description is not valid.
    */
   template <class It, class = detail::requires_iterator<It>>
   variable(It begin, It end, metadata_type meta = {}, options_type options = {},
@@ -89,16 +96,21 @@ class variable : public iterator_mixin<variable<Value, MetaData, Options, Alloca
                       (options.test(option::circular) ^ options.test(option::growth)),
                   "circular and growth options are mutually exclusive");
 
-    if (std::distance(begin, end) < 2)
-      BOOST_THROW_EXCEPTION(std::invalid_argument("bins > 0 required"));
+    const auto n = std::distance(begin, end);
+    if (n < 0)
+      BOOST_THROW_EXCEPTION(
+          std::invalid_argument("end must be reachable by incrementing begin"));
 
-    vec_.reserve(std::distance(begin, end));
+    if (n < 2) BOOST_THROW_EXCEPTION(std::invalid_argument("bins > 1 required"));
+
+    vec_.reserve(n);
     vec_.emplace_back(*begin++);
     bool strictly_ascending = true;
     for (; begin != end; ++begin) {
       strictly_ascending &= vec_.back() < *begin;
       vec_.emplace_back(*begin);
     }
+
     if (!strictly_ascending)
       BOOST_THROW_EXCEPTION(
           std::invalid_argument("input sequence must be strictly ascending"));