diff --git a/lib/sorted_set.rb b/lib/sorted_set.rb
index 8888889..80a71b2 100644
--- a/lib/sorted_set.rb
+++ b/lib/sorted_set.rb
@@ -61,3 +61,26 @@ class SortedSet < Set
 else
   require_relative 'sorted_set/ruby3'
 end
+
+if defined?(JRUBY_VERSION) || defined?(Set::CoreSet)
+  class Set
+    # Set's equality cannot see SortedSet's separate backing store.
+    module SortedSetEquality
+      def ==(other)
+        return super unless other.is_a?(SortedSet)
+
+        size == other.size && other.all? { |o| include?(o) }
+      end
+
+      def eql?(other)
+        return false if other.is_a?(SortedSet)
+
+        super
+      end
+    end
+
+    prepend SortedSetEquality
+
+    private_constant :SortedSetEquality
+  end
+end
diff --git a/lib/sorted_set/jruby.rb b/lib/sorted_set/jruby.rb
index 9456d86..c36a329 100644
--- a/lib/sorted_set/jruby.rb
+++ b/lib/sorted_set/jruby.rb
@@ -7,8 +7,13 @@
 
 class SortedSet
   def initialize(enum = nil, &block)
-    @tree = java.util.TreeSet.new
-    super
+    if block.nil? && enum.instance_of?(self.class)
+      @tree = enum.instance_variable_get(:@tree).dup
+      super(nil)
+    else
+      @tree = java.util.TreeSet.new
+      super
+    end
   end
 
   def add(o)
@@ -26,6 +31,10 @@ def delete(o)
 
   def include?(o)
     @tree.contains(o)
+  rescue Java::JavaLang::ClassCastException
+    # TreeSet rejects some Ruby-comparable cross-class values, such as
+    # Integer and Float.
+    @tree.to_a.any? { |element| (element <=> o) == 0 }
   end
   alias member? include?
 
@@ -69,6 +78,21 @@ def hash
     @tree.to_a.hash
   end
 
+  def ==(other)
+    return true if equal?(other)
+
+    if other.is_a?(Set)
+      size == other.size && other.all? { |o| include?(o) }
+    else
+      false
+    end
+  end
+
+  def eql?(other)
+    other.instance_of?(self.class) &&
+      @tree.to_a.eql?(other.instance_variable_get(:@tree).to_a)
+  end
+
   def freeze
     super
   end
diff --git a/lib/sorted_set/ruby4.rb b/lib/sorted_set/ruby4.rb
index bbdcd43..32c06bb 100644
--- a/lib/sorted_set/ruby4.rb
+++ b/lib/sorted_set/ruby4.rb
@@ -5,8 +5,13 @@
 
 class SortedSet
   def initialize(enum = nil, &block)
-    @tree = RBTree.new
-    super
+    if block.nil? && enum.instance_of?(self.class)
+      @tree = enum.instance_variable_get(:@tree).dup
+      super(nil)
+    else
+      @tree = RBTree.new
+      super
+    end
   end
 
   def add(o)
@@ -63,6 +68,23 @@ def hash
     @tree.keys.hash
   end
 
+  def ==(other)
+    return true if equal?(other)
+
+    if other.is_a?(SortedSet)
+      @tree == other.instance_variable_get(:@tree)
+    elsif other.is_a?(Set)
+      size == other.size && other.all? { |o| include?(o) }
+    else
+      false
+    end
+  end
+
+  def eql?(other)
+    other.instance_of?(self.class) &&
+      @tree.keys.eql?(other.instance_variable_get(:@tree).keys)
+  end
+
   def freeze
     @tree.freeze
     super
diff --git a/test/test_sorted_set.rb b/test/test_sorted_set.rb
index 9a3efd2..c558b76 100644
--- a/test/test_sorted_set.rb
+++ b/test/test_sorted_set.rb
@@ -121,4 +121,98 @@ def test_enumerable_to_sorted_set
     assert_instance_of(SortedSet, set)
     assert_equal([-10,-8,-6,-4,-2], set.to_a)
   end
+
+  def test_new_from_sorted_set
+    set1 = SortedSet[3,1,2]
+    set2 = SortedSet.new(set1)
+    assert_equal([1,2,3], set2.to_a)
+    assert_nothing_raised { set2.add 4 }
+    assert_equal([1,2,3,4], set2.to_a)
+    assert_equal([1,2,3], set1.to_a)
+
+    set2 = SortedSet.new(set1) { |o| o * 2 }
+    assert_equal([2,4,6], set2.to_a)
+
+    set1.freeze
+    set3 = SortedSet.new(set1)
+    assert_equal([1,2,3], set3.to_a)
+    assert_not_predicate set3, :frozen?
+    assert_nothing_raised { set3.add 4 }
+  end
+
+  def test_equality
+    omit('Ruby 4.0 specific') unless SortedSet.instance_method(:==).owner == SortedSet
+
+    set1 = SortedSet[1,2,3]
+    set2 = SortedSet[3,2,1]
+    set3 = SortedSet[1,2]
+    subclass = Class.new(SortedSet)
+    set4 = subclass.new([3,2,1])
+
+    assert_operator(set1, :==, set2)
+    assert_not_operator(set1, :==, set3)
+    assert_operator(set1, :eql?, set2)
+    assert_not_operator(set1, :eql?, set3)
+    assert_operator(set1, :==, set4)
+    assert_operator(set4, :==, set1)
+    assert_not_operator(set1, :eql?, set4)
+    assert_not_operator(set4, :eql?, set1)
+
+    assert_equal(set1.hash, set2.hash)
+
+    assert_equal(:first, { set1 => :first, set3 => :second }[set2])
+    assert_equal(:first, { first: set1, second: set3 }.key(set2))
+
+    integer_set = SortedSet[1]
+    float_set = SortedSet[1.0]
+    assert_operator(integer_set, :==, float_set)
+    assert_not_operator(integer_set, :eql?, float_set)
+    assert_nil({ integer_set => :match }[float_set])
+
+    element_class = Class.new do
+      include Comparable
+
+      attr_reader :value
+
+      def initialize(value)
+        @value = value
+      end
+
+      def <=>(other)
+        value <=> other.value
+      end
+    end
+
+    assert_operator(SortedSet[element_class.new(1)], :==, SortedSet[element_class.new(1)])
+  end
+
+  def test_equality_with_set
+    omit('Ruby 4.0 specific') unless SortedSet.instance_method(:==).owner == SortedSet
+
+    sorted_set = SortedSet[1,2,3]
+
+    assert_operator(SortedSet[], :==, Set[])
+    assert_operator(sorted_set, :==, Set[3,2,1])
+    assert_not_operator(sorted_set, :==, Set[1,2])
+    assert_not_operator(sorted_set, :==, Set[1,2,4])
+    assert_operator(SortedSet[1], :==, Set[1.0])
+    assert_include(SortedSet[1], 1.0)
+    assert_not_operator(sorted_set, :==, [1,2,3])
+    assert_not_operator(sorted_set, :eql?, Set[1,2,3])
+  end
+
+  def test_set_equality_with_sorted_set
+    omit('Ruby 4.0 specific') unless SortedSet.instance_method(:==).owner == SortedSet
+
+    sorted_set = SortedSet[1,2,3]
+
+    assert_operator(Set[], :==, SortedSet[])
+    assert_operator(Set[3,2,1], :==, sorted_set)
+    assert_not_operator(Set[1,2], :==, sorted_set)
+    assert_not_operator(Set[1,2,4], :==, sorted_set)
+    assert_not_operator(Set[1.0], :==, SortedSet[1])
+    assert_not_operator(Set[], :eql?, SortedSet[])
+    assert_not_operator(Set[1,2,3], :eql?, sorted_set)
+    assert_nil({ Set[] => :match }[SortedSet[]])
+  end
 end