diff --git a/spec/xoshiro128plus_spec.cr b/spec/xoshiro128plus_spec.cr
index 266e7e9..4e43671 100644
--- a/spec/xoshiro128plus_spec.cr
+++ b/spec/xoshiro128plus_spec.cr
@@ -76,7 +76,7 @@ describe Random::XoShiRo128Plus do
     original.next_u.should eq(0x472255cc_u32)
 
     rng = original.split
-    rng.should_not be(original)
-    rng.next_u.should eq(0xbbc0480a_u32)
+    rng.should_not eq(original)
+    rng.next_u.should eq(0x16d92aa0_u32)
   end
 end
diff --git a/spec/xoshiro128starstar_spec.cr b/spec/xoshiro128starstar_spec.cr
index d7c7da1..7f0eea5 100644
--- a/spec/xoshiro128starstar_spec.cr
+++ b/spec/xoshiro128starstar_spec.cr
@@ -73,10 +73,11 @@ describe Random::XoShiRo128StarStar do
   end
 
   it "#split" do
-    rng = Random::XoShiRo128StarStar.new(0xdeadbeef_u64)
-    rng.next_u.should eq(0xa9c3d393_u32)
+    original = Random::XoShiRo128StarStar.new(0xdeadbeef_u64)
+    original.next_u.should eq(0xa9c3d393_u32)
 
-    rng = rng.split
-    rng.next_u.should eq(0x61800258_u32)
+    rng = original.split
+    rng.should_not eq(original)
+    rng.next_u.should eq(0x818871d8_u32)
   end
 end
diff --git a/spec/xoshiro256plus_spec.cr b/spec/xoshiro256plus_spec.cr
index ba9827d..0daf865 100644
--- a/spec/xoshiro256plus_spec.cr
+++ b/spec/xoshiro256plus_spec.cr
@@ -76,7 +76,7 @@ describe Random::XoShiRo256Plus do
     original.next_u.should eq(0xbf468782e4ab532b_u64)
 
     rng = original.split
-    rng.should_not be(original)
-    rng.next_u.should eq(0xef2817c89dfe32e1_u64)
+    rng.should_not eq(original)
+    rng.next_u.should eq(0x6ecba84e8c0ab44_u64)
   end
 end
diff --git a/spec/xoshiro256starstar_spec.cr b/spec/xoshiro256starstar_spec.cr
index e81a797..c76c6c9 100644
--- a/spec/xoshiro256starstar_spec.cr
+++ b/spec/xoshiro256starstar_spec.cr
@@ -76,7 +76,7 @@ describe Random::XoShiRo256StarStar do
     original.next_u.should eq(0xc5555444a74d7e83_u64)
 
     rng = original.split
-    rng.should_not be(original)
-    rng.next_u.should eq(0x228bb75bc497d835_u64)
+    rng.should_not eq(original)
+    rng.next_u.should eq(0x54f773200a4efa23_u64)
   end
 end
diff --git a/src/splittable.cr b/src/splittable.cr
index e5cb3a0..cf52a2a 100644
--- a/src/splittable.cr
+++ b/src/splittable.cr
@@ -14,8 +14,8 @@ class Random::Splittable
 
   private GOLDEN_GAMMA = 0x9e3779b97f4a7c15_u64 # odd
 
-  @seed : UInt64
-  @gamma : UInt64
+  protected setter seed : UInt64
+  protected setter gamma : UInt64
 
   def initialize
     s = default_gen.add(2_u64 &* GOLDEN_GAMMA)
@@ -38,8 +38,9 @@ class Random::Splittable
     mix32(next_seed)
   end
 
-  def split : self
-    self.class.new(next_u, mix_gamma(next_seed))
+  def split_internal(other : self) : Nil
+    other.seed = next_u
+    other.gamma = mix_gamma(next_seed)
   end
 
   private def next_seed : UInt64
diff --git a/src/splittable128.cr b/src/splittable128.cr
index 65376b0..3e71bb3 100644
--- a/src/splittable128.cr
+++ b/src/splittable128.cr
@@ -11,8 +11,8 @@ class Random::Splittable128
   GAMMA_PRIME = (1_u64 << 57) &- 13 # "Ginny"
   GAMMA_GAMMA = 0x00281e2dba6606f3_u64
 
-  @seed_hi : UInt64
-  @seed_lo : UInt64
+  protected setter seed_hi : UInt64
+  protected setter seed_lo : UInt64
   @gamma_hi : UInt64
   @gamma_lo : UInt64
   @next_split : UInt64
@@ -26,6 +26,13 @@ class Random::Splittable128
   end
 
   def initialize(@seed_hi = next_default_seed, @seed_lo = 0_u64, s : UInt64 = GAMMA_GAMMA)
+    @gamma_hi = 0_u64
+    @gamma_lo = 0_u64
+    @next_split = 0_u64
+    mix_gamma(s)
+  end
+
+  protected def mix_gamma(s)
     # we require 0 <= s <= Ginny
     s &+= GAMMA_GAMMA
     s &-= GAMMA_PRIME if s >= GAMMA_PRIME
@@ -38,9 +45,11 @@ class Random::Splittable128
     @next_split = s
   end
 
-  def split : self
+  def split_internal(other : self) : Nil
     next_raw64
-    Splittable128.new(@seed_hi, @seed_lo, @next_split)
+    other.seed_hi = @seed_hi
+    other.seed_lo = @seed_lo
+    other.mix_gamma(@next_split)
   end
 
   def next_u : UInt64
diff --git a/src/xoshiro128.cr b/src/xoshiro128.cr
index 379d683..941ea91 100644
--- a/src/xoshiro128.cr
+++ b/src/xoshiro128.cr
@@ -121,9 +121,9 @@ abstract class Random::XoShiRo128
     @state.to_unsafe[3] = s3
   end
 
-  # Returns a new instance that shares no mutable state with this instance.
-  def split
+  def split_internal(other : self) : Nil
     self.class.new(@state.map { |s| murmurhash3(s) })
+    other.next_u
   end
 
   @[AlwaysInline]
diff --git a/src/xoshiro256.cr b/src/xoshiro256.cr
index 66a87af..2c0730c 100644
--- a/src/xoshiro256.cr
+++ b/src/xoshiro256.cr
@@ -110,12 +110,9 @@ abstract class Random::XoShiRo256
     @state.to_unsafe[3] = s3
   end
 
-  # Returns a new instance that shares no mutable state with this instance. The
-  # sequence generated by the new instance depends deterministically from the
-  # state of this instance, but the probability that the sequence generated by
-  # this instance and by the new instance overlap is negligible.
-  def split
-    self.class.new(@state.map { |s| murmurhash3(s) })
+  def split_internal(other : self) : Nil
+    @state.map! { |s| murmurhash3(s) }
+    other.next_u
   end
 
   @[AlwaysInline]