diff --git a/lib/tdigest/tdigest.rb b/lib/tdigest/tdigest.rb
index 17c09ac..bf25eba 100644
--- a/lib/tdigest/tdigest.rb
+++ b/lib/tdigest/tdigest.rb
@@ -16,6 +16,16 @@ def initialize(delta = 0.01, k = 25, cx = 1.1)
       reset!
     end
 
+    def +(other)
+      # Uses delta, k and cx from the caller
+      t = self.class.new(@delta, @k, @cx)
+      data = self.centroids.values + other.centroids.values
+      while data.length > 0
+        t.push_centroid(data.delete_at(rand(data.length)))
+      end
+      t
+    end
+
     def as_bytes
       # compression as defined by Java implementation
       size = @centroids.size
@@ -117,6 +127,13 @@ def find_nearest(x)
       end
     end
 
+    def merge!(other)
+      # Uses delta, k and cx from the caller
+      t = self + other
+      @centroids = t.centroids
+      compress!
+    end
+
     def p_rank(x)
       is_array = x.is_a? Array
       x = [x] unless is_array
@@ -312,6 +329,14 @@ def _digest(x, n)
 
       _cumulate(false)
 
+      # If the number of centroids has grown to a very large size,
+      # it may be due to values being inserted in sorted order.
+      # We combat that by replaying the centroids in random order,
+      # which is what compress! does
+      if @centroids.size > (@k / @delta)
+        compress!
+      end
+
       nil
     end
 
diff --git a/test/tdigest_test.rb b/test/tdigest_test.rb
index a673b41..76508d4 100644
--- a/test/tdigest_test.rb
+++ b/test/tdigest_test.rb
@@ -82,9 +82,11 @@ def test_that_it_has_a_version_number
 
     describe 'with alot of uniformly distributed points' do
       it 'has minimal error' do
+        seed = srand(1234) # Makes the values a proper fixture
         N = 100_000
         maxerr = 0
         values = Array.new(N).map { rand }
+        srand(seed)
 
         tdigest.push(values)
         tdigest.compress!
@@ -135,6 +137,13 @@ def test_that_it_has_a_version_number
         123829787.23404256,
         103191489.36170213]
     end
+
+    it 'does not blow up if data comes in sorted' do
+      tdigest.push(0..10_000)
+      tdigest.centroids.size.must_be :<, 5_000
+      tdigest.compress!
+      tdigest.centroids.size.must_be :<, 1_000
+    end
   end
 
   describe '#size' do
@@ -145,4 +154,77 @@ def test_that_it_has_a_version_number
       tdigest.size.must_equal n
     end
   end
+
+  describe '#+' do
+    it 'works with empty tdigests' do
+      other = ::TDigest::TDigest.new(0.001, 50, 1.2)
+      (tdigest + other).centroids.size.must_equal 0
+    end
+
+    describe 'adding two tdigests' do
+      before do
+        @other = ::TDigest::TDigest.new(0.001, 50, 1.2)
+        [tdigest, @other].each do |td|
+          td.push(60, 100)
+          10.times { td.push(rand * 100) }
+        end
+      end
+
+      it 'has the parameters of the left argument (the calling tdigest)' do
+        new_tdigest = tdigest + @other
+        new_tdigest.instance_variable_get(:@delta).must_equal tdigest.instance_variable_get(:@delta)
+        new_tdigest.instance_variable_get(:@k).must_equal tdigest.instance_variable_get(:@k)
+        new_tdigest.instance_variable_get(:@cx).must_equal tdigest.instance_variable_get(:@cx)
+      end
+
+      it 'results in a tdigest with number of centroids less than or equal to the combined centroids size' do
+        new_tdigest = tdigest + @other
+        new_tdigest.centroids.size.must_be :<=, tdigest.centroids.size + @other.centroids.size
+      end
+
+      it 'has the size of the two digests combined' do
+        new_tdigest = tdigest + @other
+        new_tdigest.size.must_equal (tdigest.size + @other.size)
+      end
+    end
+  end
+
+  describe '#merge!' do
+    it 'works with empty tdigests' do
+      other = ::TDigest::TDigest.new(0.001, 50, 1.2)
+      tdigest.merge!(other)
+      (tdigest).centroids.size.must_equal 0
+    end
+
+    describe 'with populated tdigests' do
+      before do
+        @other = ::TDigest::TDigest.new(0.001, 50, 1.2)
+        [tdigest, @other].each do |td|
+          td.push(60, 100)
+          10.times { td.push(rand * 100) }
+        end
+      end
+
+      it 'has the parameters of the calling tdigest' do
+        vars = [:@delta, :@k, :@cs]
+        expected = Hash[vars.map { |v| [v, tdigest.instance_variable_get(v)] }]
+        tdigest.merge!(@other)
+        vars.each do |v|
+          tdigest.instance_variable_get(v).must_equal expected[v]
+        end
+      end
+
+      it 'results in a tdigest with number of centroids less than or equal to the combined centroids size' do
+        combined_size = tdigest.centroids.size + @other.centroids.size
+        tdigest.merge!(@other)
+        tdigest.centroids.size.must_be :<=, combined_size
+      end
+
+      it 'has the size of the two digests combined' do
+        combined_size = tdigest.size + @other.size
+        tdigest.merge!(@other)
+        tdigest.size.must_equal combined_size
+      end
+    end
+  end
 end