diff --git a/README.md b/README.md
index e3da0c9..eefc06f 100644
--- a/README.md
+++ b/README.md
@@ -25,14 +25,15 @@
 
 ## Installation
 
-[flat.hpp][flat] is a header only library. All you need to do is copy the header files (`flat_set.hpp` and `flat_map.hpp`) into your project and include them:
+[flat.hpp][flat] is a header only library. All you need to do is copy the header files (`flat_set.hpp` and `flat_map.hpp`) into your project and include them.
 
-```cpp
-#include "flat_set.hpp"
-#include "flat_map.hpp"
-```
+## API
+- [Flat Set](#flat-set)
+- [Flat Map](#flat-map)
+- [Flat Multiset](#flat-multiset)
+- [Flat Multimap](#flat-multimap)
 
-## flat_set
+## Flat Set
 
 ```cpp
 template < typename Key
@@ -131,6 +132,9 @@ const_reverse_iterator crend() const noexcept;
 bool empty() const noexcept;
 size_type size() const noexcept;
 size_type max_size() const noexcept;
+size_type capacity() const noexcept;
+void reserve(size_type ncapacity);
+void shrink_to_fit();
 ```
 
 ### Modifiers
@@ -223,7 +227,7 @@ bool operator>=(
     const flat_set<K, C, A>& r);
 ```
 
-## flat_map
+## Flat Map
 
 ```cpp
 template < typename Key
@@ -329,6 +333,9 @@ const_reverse_iterator crend() const noexcept;
 bool empty() const noexcept;
 size_type size() const noexcept;
 size_type max_size() const noexcept;
+size_type capacity() const noexcept;
+void reserve(size_type ncapacity);
+void shrink_to_fit();
 ```
 
 ### Element access
@@ -431,4 +438,12 @@ bool operator>=(
     const flat_map<K, V, C, A>& r);
 ```
 
+## Flat Multiset
+
+> coming soon!
+
+## Flat Multimap
+
+> coming soon!
+
 ## [License (MIT)](./LICENSE.md)
diff --git a/flat_map.hpp b/flat_map.hpp
index 7b19608..c5a5e94 100644
--- a/flat_map.hpp
+++ b/flat_map.hpp
@@ -192,6 +192,18 @@ namespace flat_hpp
             return data_.max_size();
         }
 
+        size_type capacity() const noexcept {
+            return data_.capacity();
+        }
+
+        void reserve(size_type ncapacity) {
+            data_.reserve(ncapacity);
+        }
+
+        void shrink_to_fit() {
+            data_.shrink_to_fit();
+        }
+
         mapped_type& operator[](key_type&& key) {
             const iterator iter = find(key);
             return iter != end()
@@ -354,39 +366,88 @@ namespace flat_hpp
 
 namespace flat_hpp
 {
-    template < typename K, typename V, typename C, typename A >
-    void swap(flat_map<K, V, C, A>& l, flat_map<K, V, C, A>& r) {
+    template < typename Key
+             , typename Value
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    void swap(
+        flat_map<Key, Value, Compare, Allocator, Container>& l,
+        flat_map<Key, Value, Compare, Allocator, Container>& r)
+    {
         l.swap(r);
     }
 
-    template < typename K, typename V, typename C, typename A >
-    bool operator==(const flat_map<K, V, C, A>& l, const flat_map<K, V, C, A>& r) {
+    template < typename Key
+             , typename Value
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    bool operator==(
+        const flat_map<Key, Value, Compare, Allocator, Container>& l,
+        const flat_map<Key, Value, Compare, Allocator, Container>& r)
+    {
         return l.size() == r.size()
             && std::equal(l.begin(), l.end(), r.begin(), r.end());
     }
 
-    template < typename K, typename V, typename C, typename A >
-    bool operator!=(const flat_map<K, V, C, A>& l, const flat_map<K, V, C, A>& r) {
+    template < typename Key
+             , typename Value
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    bool operator!=(
+        const flat_map<Key, Value, Compare, Allocator, Container>& l,
+        const flat_map<Key, Value, Compare, Allocator, Container>& r)
+    {
         return !(l == r);
     }
 
-    template < typename K, typename V, typename C, typename A >
-    bool operator<(const flat_map<K, V, C, A>& l, const flat_map<K, V, C, A>& r) {
+    template < typename Key
+             , typename Value
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    bool operator<(
+        const flat_map<Key, Value, Compare, Allocator, Container>& l,
+        const flat_map<Key, Value, Compare, Allocator, Container>& r)
+    {
         return std::lexicographical_compare(l.begin(), l.end(), r.begin(), r.end());
     }
 
-    template < typename K, typename V, typename C, typename A >
-    bool operator>(const flat_map<K, V, C, A>& l, const flat_map<K, V, C, A>& r) {
+    template < typename Key
+             , typename Value
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    bool operator>(
+        const flat_map<Key, Value, Compare, Allocator, Container>& l,
+        const flat_map<Key, Value, Compare, Allocator, Container>& r)
+    {
         return r < l;
     }
 
-    template < typename K, typename V, typename C, typename A >
-    bool operator<=(const flat_map<K, V, C, A>& l, const flat_map<K, V, C, A>& r) {
+    template < typename Key
+             , typename Value
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    bool operator<=(
+        const flat_map<Key, Value, Compare, Allocator, Container>& l,
+        const flat_map<Key, Value, Compare, Allocator, Container>& r)
+    {
         return !(r < l);
     }
 
-    template < typename K, typename V, typename C, typename A >
-    bool operator>=(const flat_map<K, V, C, A>& l, const flat_map<K, V, C, A>& r) {
+    template < typename Key
+             , typename Value
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    bool operator>=(
+        const flat_map<Key, Value, Compare, Allocator, Container>& l,
+        const flat_map<Key, Value, Compare, Allocator, Container>& r)
+    {
         return !(l < r);
     }
 }
diff --git a/flat_map_tests.cpp b/flat_map_tests.cpp
index cdacde3..9424e42 100644
--- a/flat_map_tests.cpp
+++ b/flat_map_tests.cpp
@@ -7,6 +7,8 @@
 #define CATCH_CONFIG_FAST_COMPILE
 #include "catch.hpp"
 
+#include <deque>
+
 #include "flat_map.hpp"
 using namespace flat_hpp;
 
@@ -15,8 +17,20 @@ namespace
     template < typename T >
     class dummy_allocator {
     public:
+        using size_type = std::size_t;
+        using difference_type = std::ptrdiff_t;
+        using pointer = T*;
+        using const_pointer = const T*;
+        using reference = T&;
+        using const_reference = const T&;
         using value_type = T;
 
+        using propagate_on_container_move_assignment = std::true_type;
+        using is_always_equal = std::true_type;
+
+        template < typename U >
+        struct rebind { using other = dummy_allocator<U>; };
+
         dummy_allocator() = default;
         dummy_allocator(int i) : i(i) {}
 
@@ -34,6 +48,15 @@ namespace
             std::free(p);
         }
 
+        template < typename U, typename... Args >
+        void construct(U* p, Args&&... args) {
+            ::new((void*)p) U(std::forward<Args>(args)...);
+        }
+
+        void destroy(pointer p) {
+            p->~T();
+        }
+
         int i = 0;
     };
 
@@ -174,29 +197,60 @@ TEST_CASE("flat_map") {
     }
     SECTION("capacity") {
         using map_t = flat_map<int, unsigned>;
-        map_t s0;
 
-        REQUIRE(s0.empty());
-        REQUIRE_FALSE(s0.size());
-        REQUIRE(s0.max_size() == std::allocator<std::pair<int,unsigned>>().max_size());
+        {
+            map_t s0;
 
-        s0.insert({2,42});
+            REQUIRE(s0.empty());
+            REQUIRE_FALSE(s0.size());
+            REQUIRE(s0.max_size() == std::allocator<std::pair<int,unsigned>>().max_size());
 
-        REQUIRE_FALSE(s0.empty());
-        REQUIRE(s0.size() == 1u);
-        REQUIRE(s0.max_size() == std::allocator<std::pair<int,unsigned>>().max_size());
+            s0.insert({2,42});
 
-        s0.insert({2,84});
-        REQUIRE(s0.size() == 1u);
+            REQUIRE_FALSE(s0.empty());
+            REQUIRE(s0.size() == 1u);
+            REQUIRE(s0.max_size() == std::allocator<std::pair<int,unsigned>>().max_size());
 
-        s0.insert({3,84});
-        REQUIRE(s0.size() == 2u);
+            s0.insert({2,84});
+            REQUIRE(s0.size() == 1u);
 
-        s0.clear();
+            s0.insert({3,84});
+            REQUIRE(s0.size() == 2u);
 
-        REQUIRE(s0.empty());
-        REQUIRE_FALSE(s0.size());
-        REQUIRE(s0.max_size() == std::allocator<std::pair<int,unsigned>>().max_size());
+            s0.clear();
+
+            REQUIRE(s0.empty());
+            REQUIRE_FALSE(s0.size());
+            REQUIRE(s0.max_size() == std::allocator<std::pair<int,unsigned>>().max_size());
+        }
+
+        {
+            map_t s0;
+
+            REQUIRE(s0.capacity() == 0);
+            s0.reserve(42);
+            REQUIRE(s0.capacity() == 42);
+            s0.insert({{1,2},{2,3},{3,4}});
+            REQUIRE(s0.capacity() == 42);
+            s0.shrink_to_fit();
+            REQUIRE(s0.size() == 3);
+            REQUIRE(s0.capacity() == 3);
+            REQUIRE(s0 == map_t{{1,2},{2,3},{3,4}});
+
+            using alloc2_t = dummy_allocator<
+                std::pair<int, unsigned>>;
+
+            using map2_t = flat_map<
+                int,
+                unsigned,
+                std::less<int>,
+                alloc2_t,
+                std::deque<std::pair<int, unsigned>, alloc2_t>>;
+
+            map2_t s1;
+            s1.insert({{1,2},{2,3},{3,4}});
+            REQUIRE(s1 == map2_t{{1,2},{2,3},{3,4}});
+        }
     }
     SECTION("access") {
         struct obj_t {
@@ -225,6 +279,10 @@ TEST_CASE("flat_map") {
         REQUIRE(s0[1] == 84);
         REQUIRE(s0 == map_t{{1,84}});
 
+        s0[2] = 21;
+        REQUIRE(s0[2] == 21);
+        REQUIRE(s0 == map_t{{1,84},{2,21}});
+
         REQUIRE(s0.at(1) == 84);
         REQUIRE(my_as_const(s0).at(k1) == 84);
         REQUIRE_THROWS_AS(s0.at(0), std::out_of_range);
@@ -394,5 +452,13 @@ TEST_CASE("flat_map") {
         REQUIRE(map_t{{1,2},{3,4}} <= map_t{{1,2},{3,4}});
         REQUIRE_FALSE(map_t{{1,2},{3,4}} > map_t{{1,2},{3,4}});
         REQUIRE(map_t{{1,2},{3,4}} >= map_t{{1,2},{3,4}});
+
+        const map_t s0;
+        REQUIRE(s0 == s0);
+        REQUIRE_FALSE(s0 != s0);
+        REQUIRE_FALSE(s0 < s0);
+        REQUIRE_FALSE(s0 > s0);
+        REQUIRE(s0 <= s0);
+        REQUIRE(s0 >= s0);
     }
 }
diff --git a/flat_set.hpp b/flat_set.hpp
index a63e51e..c908d1f 100644
--- a/flat_set.hpp
+++ b/flat_set.hpp
@@ -170,6 +170,18 @@ namespace flat_hpp
             return data_.max_size();
         }
 
+        size_type capacity() const noexcept {
+            return data_.capacity();
+        }
+
+        void reserve(size_type ncapacity) {
+            data_.reserve(ncapacity);
+        }
+
+        void shrink_to_fit() {
+            data_.shrink_to_fit();
+        }
+
         std::pair<iterator, bool> insert(value_type&& value) {
             const iterator iter = lower_bound(value);
             return iter == end() || compare_(value, *iter)
@@ -302,39 +314,81 @@ namespace flat_hpp
 
 namespace flat_hpp
 {
-    template < typename K, typename C, typename A >
-    void swap(flat_set<K, C, A>& l, flat_set<K, C, A>& r) {
+    template < typename Key
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    void swap(
+        flat_set<Key, Compare, Allocator, Container>& l,
+        flat_set<Key, Compare, Allocator, Container>& r)
+    {
         l.swap(r);
     }
 
-    template < typename K, typename C, typename A >
-    bool operator==(const flat_set<K, C, A>& l, const flat_set<K, C, A>& r) {
+    template < typename Key
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    bool operator==(
+        const flat_set<Key, Compare, Allocator, Container>& l,
+        const flat_set<Key, Compare, Allocator, Container>& r)
+    {
         return l.size() == r.size()
             && std::equal(l.begin(), l.end(), r.begin(), r.end());
     }
 
-    template < typename K, typename C, typename A >
-    bool operator!=(const flat_set<K, C, A>& l, const flat_set<K, C, A>& r) {
+    template < typename Key
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    bool operator!=(
+        const flat_set<Key, Compare, Allocator, Container>& l,
+        const flat_set<Key, Compare, Allocator, Container>& r)
+    {
         return !(l == r);
     }
 
-    template < typename K, typename C, typename A >
-    bool operator<(const flat_set<K, C, A>& l, const flat_set<K, C, A>& r) {
+    template < typename Key
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    bool operator<(
+        const flat_set<Key, Compare, Allocator, Container>& l,
+        const flat_set<Key, Compare, Allocator, Container>& r)
+    {
         return std::lexicographical_compare(l.begin(), l.end(), r.begin(), r.end());
     }
 
-    template < typename K, typename C, typename A >
-    bool operator>(const flat_set<K, C, A>& l, const flat_set<K, C, A>& r) {
+    template < typename Key
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    bool operator>(
+        const flat_set<Key, Compare, Allocator, Container>& l,
+        const flat_set<Key, Compare, Allocator, Container>& r)
+    {
         return r < l;
     }
 
-    template < typename K, typename C, typename A >
-    bool operator<=(const flat_set<K, C, A>& l, const flat_set<K, C, A>& r) {
+    template < typename Key
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    bool operator<=(
+        const flat_set<Key, Compare, Allocator, Container>& l,
+        const flat_set<Key, Compare, Allocator, Container>& r)
+    {
         return !(r < l);
     }
 
-    template < typename K, typename C, typename A >
-    bool operator>=(const flat_set<K, C, A>& l, const flat_set<K, C, A>& r) {
+    template < typename Key
+             , typename Compare
+             , typename Allocator
+             , typename Container >
+    bool operator>=(
+        const flat_set<Key, Compare, Allocator, Container>& l,
+        const flat_set<Key, Compare, Allocator, Container>& r)
+    {
         return !(l < r);
     }
 }
diff --git a/flat_set_tests.cpp b/flat_set_tests.cpp
index 5331c3c..54e2f2e 100644
--- a/flat_set_tests.cpp
+++ b/flat_set_tests.cpp
@@ -7,6 +7,8 @@
 #define CATCH_CONFIG_FAST_COMPILE
 #include "catch.hpp"
 
+#include <deque>
+
 #include "flat_set.hpp"
 using namespace flat_hpp;
 
@@ -15,8 +17,20 @@ namespace
     template < typename T >
     class dummy_allocator {
     public:
+        using size_type = std::size_t;
+        using difference_type = std::ptrdiff_t;
+        using pointer = T*;
+        using const_pointer = const T*;
+        using reference = T&;
+        using const_reference = const T&;
         using value_type = T;
 
+        using propagate_on_container_move_assignment = std::true_type;
+        using is_always_equal = std::true_type;
+
+        template < typename U >
+        struct rebind { using other = dummy_allocator<U>; };
+
         dummy_allocator() = default;
         dummy_allocator(int i) : i(i) {}
 
@@ -34,6 +48,15 @@ namespace
             std::free(p);
         }
 
+        template < typename U, typename... Args >
+        void construct(U* p, Args&&... args) {
+            ::new((void*)p) U(std::forward<Args>(args)...);
+        }
+
+        void destroy(pointer p) {
+            p->~T();
+        }
+
         int i = 0;
     };
 
@@ -158,29 +181,58 @@ TEST_CASE("flat_set") {
     }
     SECTION("capacity") {
         using set_t = flat_set<int>;
-        set_t s0;
 
-        REQUIRE(s0.empty());
-        REQUIRE_FALSE(s0.size());
-        REQUIRE(s0.max_size() == std::allocator<int>().max_size());
+        {
+            set_t s0;
 
-        s0.insert(42);
+            REQUIRE(s0.empty());
+            REQUIRE_FALSE(s0.size());
+            REQUIRE(s0.max_size() == std::allocator<int>().max_size());
 
-        REQUIRE_FALSE(s0.empty());
-        REQUIRE(s0.size() == 1u);
-        REQUIRE(s0.max_size() == std::allocator<int>().max_size());
+            s0.insert(42);
 
-        s0.insert(42);
-        REQUIRE(s0.size() == 1u);
+            REQUIRE_FALSE(s0.empty());
+            REQUIRE(s0.size() == 1u);
+            REQUIRE(s0.max_size() == std::allocator<int>().max_size());
 
-        s0.insert(84);
-        REQUIRE(s0.size() == 2u);
+            s0.insert(42);
+            REQUIRE(s0.size() == 1u);
 
-        s0.clear();
+            s0.insert(84);
+            REQUIRE(s0.size() == 2u);
 
-        REQUIRE(s0.empty());
-        REQUIRE_FALSE(s0.size());
-        REQUIRE(s0.max_size() == std::allocator<int>().max_size());
+            s0.clear();
+
+            REQUIRE(s0.empty());
+            REQUIRE_FALSE(s0.size());
+            REQUIRE(s0.max_size() == std::allocator<int>().max_size());
+        }
+
+        {
+            set_t s0;
+
+            REQUIRE(s0.capacity() == 0);
+            s0.reserve(42);
+            REQUIRE(s0.capacity() == 42);
+            s0.insert({1,2,3});
+            REQUIRE(s0.capacity() == 42);
+            s0.shrink_to_fit();
+            REQUIRE(s0.size() == 3);
+            REQUIRE(s0.capacity() == 3);
+            REQUIRE(s0 == set_t{1,2,3});
+
+            using alloc2_t = dummy_allocator<int>;
+
+            using set2_t = flat_set<
+                int,
+                std::less<int>,
+                alloc2_t,
+                std::deque<int, alloc2_t>>;
+
+            set2_t s1;
+            s1.insert({1,2,3});
+            REQUIRE(s1 == set2_t{1,2,3});
+        }
     }
     SECTION("inserts") {
         struct obj_t {
@@ -365,5 +417,13 @@ TEST_CASE("flat_set") {
         REQUIRE(set_t{1,2,3} <= set_t{1,2,3});
         REQUIRE_FALSE(set_t{1,2,3} > set_t{1,2,3});
         REQUIRE(set_t{1,2,3} >= set_t{1,2,3});
+
+        const set_t s0;
+        REQUIRE(s0 == s0);
+        REQUIRE_FALSE(s0 != s0);
+        REQUIRE_FALSE(s0 < s0);
+        REQUIRE_FALSE(s0 > s0);
+        REQUIRE(s0 <= s0);
+        REQUIRE(s0 >= s0);
     }
 }