diff --git a/core/src/main/scala/cats/Eval.scala b/core/src/main/scala/cats/Eval.scala
index 91c142bf0e..bf6529d3c3 100644
--- a/core/src/main/scala/cats/Eval.scala
+++ b/core/src/main/scala/cats/Eval.scala
@@ -72,28 +72,28 @@ sealed abstract class Eval[+A] extends Serializable { self =>
    */
   def flatMap[B](f: A => Eval[B]): Eval[B] =
     this match {
-      case c: Eval.Compute[A] =>
-        new Eval.Compute[B] {
+      case c: Eval.FlatMap[A] =>
+        new Eval.FlatMap[B] {
           type Start = c.Start
           // See https://issues.scala-lang.org/browse/SI-9931 for an explanation
           // of why the type annotations are necessary in these two lines on
           // Scala 2.12.0.
           val start: () => Eval[Start] = c.start
           val run: Start => Eval[B] = (s: c.Start) =>
-            new Eval.Compute[B] {
+            new Eval.FlatMap[B] {
               type Start = A
               val start = () => c.run(s)
               val run = f
             }
         }
-      case c: Eval.Call[A] =>
-        new Eval.Compute[B] {
+      case c: Eval.Defer[A] =>
+        new Eval.FlatMap[B] {
           type Start = A
           val start = c.thunk
           val run = f
         }
       case _ =>
-        new Eval.Compute[B] {
+        new Eval.FlatMap[B] {
           type Start = A
           val start = () => self
           val run = f
@@ -203,7 +203,7 @@ object Eval extends EvalInstances {
    * which produces an Eval[A] value. Like .flatMap, it is stack-safe.
    */
   def defer[A](a: => Eval[A]): Eval[A] =
-    new Eval.Call[A](a _) {}
+    new Eval.Defer[A](a _) {}
 
   /**
    * Static Eval instance for common value `Unit`.
@@ -246,47 +246,52 @@ object Eval extends EvalInstances {
   val One: Eval[Int] = Now(1)
 
   /**
-   * Call is a type of Eval[A] that is used to defer computations
+   * Defer is a type of Eval[A] that is used to defer computations
    * which produce Eval[A].
    *
-   * Users should not instantiate Call instances themselves. Instead,
+   * Users should not instantiate Defer instances themselves. Instead,
    * they will be automatically created when needed.
    */
-  sealed abstract class Call[A](val thunk: () => Eval[A]) extends Eval[A] {
-    def memoize: Eval[A] = new Later(() => value)
-    def value: A = Call.loop(this).value
-  }
+  sealed abstract class Defer[A](val thunk: () => Eval[A]) extends Eval[A] {
 
-  object Call {
+    def memoize: Eval[A] = Memoize(this)
+    def value: A = evaluate(this)
+  }
 
-    /**
-     * Collapse the call stack for eager evaluations.
-     */
-    @tailrec private def loop[A](fa: Eval[A]): Eval[A] = fa match {
-      case call: Eval.Call[A] =>
-        loop(call.thunk())
-      case compute: Eval.Compute[A] =>
-        new Eval.Compute[A] {
+  /**
+   * Advance until we find a non-deferred Eval node.
+   *
+   * Often we may have deep chains of Defer nodes; the goal here is to
+   * advance through those to find the underlying "work" (in the case
+   * of FlatMap nodes) or "value" (in the case of Now, Later, or
+   * Always nodes).
+   */
+  @tailrec private def advance[A](fa: Eval[A]): Eval[A] =
+    fa match {
+      case call: Eval.Defer[A] =>
+        advance(call.thunk())
+      case compute: Eval.FlatMap[A] =>
+        new Eval.FlatMap[A] {
           type Start = compute.Start
           val start: () => Eval[Start] = () => compute.start()
-          val run: Start => Eval[A] = s => loop1(compute.run(s))
+          val run: Start => Eval[A] = s => advance1(compute.run(s))
         }
       case other => other
     }
 
-    /**
-     * Alias for loop that can be called in a non-tail position
-     * from an otherwise tailrec-optimized loop.
-     */
-    private def loop1[A](fa: Eval[A]): Eval[A] = loop(fa)
-  }
+  /**
+   * Alias for advance that can be called in a non-tail position
+   * from an otherwise tailrec-optimized advance.
+   */
+  private def advance1[A](fa: Eval[A]): Eval[A] =
+    advance(fa)
 
   /**
-   * Compute is a type of Eval[A] that is used to chain computations
+   * FlatMap is a type of Eval[A] that is used to chain computations
    * involving .map and .flatMap. Along with Eval#flatMap it
    * implements the trampoline that guarantees stack-safety.
    *
-   * Users should not instantiate Compute instances
+   * Users should not instantiate FlatMap instances
    * themselves. Instead, they will be automatically created when
    * needed.
    *
@@ -294,35 +299,77 @@ object Eval extends EvalInstances {
    * trampoline are not exposed. This allows a slightly more efficient
    * implementation of the .value method.
    */
-  sealed abstract class Compute[A] extends Eval[A] {
+  sealed abstract class FlatMap[A] extends Eval[A] { self =>
     type Start
     val start: () => Eval[Start]
     val run: Start => Eval[A]
 
-    def memoize: Eval[A] = Later(value)
-
-    def value: A = {
-      type L = Eval[Any]
-      type C = Any => Eval[Any]
-      @tailrec def loop(curr: L, fs: List[C]): Any =
-        curr match {
-          case c: Compute[_] =>
-            c.start() match {
-              case cc: Compute[_] =>
-                loop(
-                  cc.start().asInstanceOf[L],
-                  cc.run.asInstanceOf[C] :: c.run.asInstanceOf[C] :: fs)
-              case xx =>
-                loop(c.run(xx.value), fs)
-            }
-          case x =>
-            fs match {
-              case f :: fs => loop(f(x.value), fs)
-              case Nil => x.value
-            }
-        }
-      loop(this.asInstanceOf[L], Nil).asInstanceOf[A]
+    def memoize: Eval[A] = Memoize(this)
+    def value: A = evaluate(this)
+  }
+
+  private case class Memoize[A](eval: Eval[A]) extends Eval[A] {
+    var result: Option[A] = None
+    def memoize: Eval[A] = this
+    def value: A =
+      result match {
+        case Some(a) => a
+        case None =>
+          val a = evaluate(this)
+          result = Some(a)
+          a
+      }
+  }
+
+
+  private def evaluate[A](e: Eval[A]): A = {
+    type L = Eval[Any]
+    type M = Memoize[Any]
+    type C = Any => Eval[Any]
+
+    def addToMemo(m: M): C = { a: Any =>
+      m.result = Some(a)
+      Now(a)
     }
+
+    @tailrec def loop(curr: L, fs: List[C]): Any =
+      curr match {
+        case c: FlatMap[_] =>
+          c.start() match {
+            case cc: FlatMap[_] =>
+              loop(
+                cc.start().asInstanceOf[L],
+                cc.run.asInstanceOf[C] :: c.run.asInstanceOf[C] :: fs)
+            case mm@Memoize(eval) =>
+              mm.result match {
+                case Some(a) =>
+                  loop(Now(a), c.run.asInstanceOf[C] :: fs)
+                case None =>
+                  loop(eval, addToMemo(mm.asInstanceOf[M]) :: c.run.asInstanceOf[C] :: fs)
+              }
+            case xx =>
+              loop(c.run(xx.value), fs)
+          }
+        case call: Defer[_] =>
+          loop(advance(call), fs)
+        case m@Memoize(eval) =>
+          m.result match {
+            case Some(a) =>
+              fs match {
+                case f :: fs => loop(f(a), fs)
+                case Nil => a
+              }
+            case None =>
+              loop(eval, addToMemo(m) :: fs)
+          }
+        case x =>
+          fs match {
+            case f :: fs => loop(f(x.value), fs)
+            case Nil => x.value
+          }
+      }
+
+    loop(e.asInstanceOf[L], Nil).asInstanceOf[A]
   }
 }
 
diff --git a/laws/src/main/scala/cats/laws/discipline/Arbitrary.scala b/laws/src/main/scala/cats/laws/discipline/Arbitrary.scala
index 679d2028a5..ba14df7cd5 100644
--- a/laws/src/main/scala/cats/laws/discipline/Arbitrary.scala
+++ b/laws/src/main/scala/cats/laws/discipline/Arbitrary.scala
@@ -90,9 +90,9 @@ object arbitrary extends ArbitraryInstances0 {
 
   implicit def catsLawsArbitraryForEval[A: Arbitrary]: Arbitrary[Eval[A]] =
     Arbitrary(Gen.oneOf(
-      getArbitrary[A].map(Eval.now(_)),
-      getArbitrary[A].map(Eval.later(_)),
-      getArbitrary[A].map(Eval.always(_))))
+      getArbitrary[A].map(a => Eval.now(a)),
+      getArbitrary[() => A].map(f => Eval.later(f())),
+      getArbitrary[() => A].map(f => Eval.always(f()))))
 
   implicit def catsLawsCogenForEval[A: Cogen]: Cogen[Eval[A]] =
     Cogen[A].contramap(_.value)
diff --git a/tests/src/test/scala/cats/tests/EvalTests.scala b/tests/src/test/scala/cats/tests/EvalTests.scala
index d67d6500a6..a49ba4a3af 100644
--- a/tests/src/test/scala/cats/tests/EvalTests.scala
+++ b/tests/src/test/scala/cats/tests/EvalTests.scala
@@ -1,11 +1,14 @@
 package cats
 package tests
 
-import scala.math.min
 import cats.laws.ComonadLaws
 import cats.laws.discipline.{BimonadTests, CartesianTests, ReducibleTests, SerializableTests}
 import cats.laws.discipline.arbitrary._
 import cats.kernel.laws.{GroupLaws, OrderLaws}
+import org.scalacheck.{Arbitrary, Cogen, Gen}
+import org.scalacheck.Arbitrary.arbitrary
+import scala.annotation.tailrec
+import scala.math.min
 
 class EvalTests extends CatsSuite {
   implicit val eqThrow: Eq[Throwable] = Eq.allEqual
@@ -140,4 +143,108 @@ class EvalTests extends CatsSuite {
       isEq.lhs should === (isEq.rhs)
     }
   }
+
+  // the following machinery is all to faciliate testing deeply-nested
+  // eval values for stack safety. the idea is that we want to
+  // randomly generate deep chains of eval operations.
+  //
+  // there are three ways to construct Eval[A] values from expressions
+  // returning A (and which are generated by Arbitrary[Eval[A]]):
+  //
+  //   - Eval.now(...)
+  //   - Eval.later(...)
+  //   - Eval.always(...)
+  //
+  // there are four operations that transform expressions returning
+  // Eval[A] into a new Eval[A] value:
+  //
+  //   - (...).map(f)
+  //   - (...).flatMap(g)
+  //   - (...).memoize
+  //   - Eval.defer(...)
+  //
+  // the O[A] ast represents these four operations. we generate a very
+  // long Vector[O[A]] and a starting () => Eval[A] expression (which
+  // we call a "leaf") and then compose these to produce one
+  // (deeply-nested) Eval[A] value, which we wrap in DeepEval(_).
+
+  case class DeepEval[A](eval: Eval[A])
+
+  object DeepEval {
+
+    sealed abstract class O[A]
+
+    case class OMap[A](f: A => A) extends O[A]
+    case class OFlatMap[A](f: A => Eval[A]) extends O[A]
+    case class OMemoize[A]() extends O[A]
+    case class ODefer[A]() extends O[A]
+
+    implicit def arbitraryO[A: Arbitrary: Cogen]: Arbitrary[O[A]] =
+      Arbitrary(Gen.oneOf(
+        arbitrary[A => A].map(OMap(_)),
+        arbitrary[A => Eval[A]].map(OFlatMap(_)),
+        Gen.const(OMemoize[A]),
+        Gen.const(ODefer[A])))
+
+    def build[A](leaf: () => Eval[A], os: Vector[O[A]]): DeepEval[A] = {
+
+      def restart(i: Int, leaf: () => Eval[A], cbs: List[Eval[A] => Eval[A]]): Eval[A] =
+        step(i, leaf, cbs)
+
+      @tailrec def step(i: Int, leaf: () => Eval[A], cbs: List[Eval[A] => Eval[A]]): Eval[A] =
+        if (i >= os.length) cbs.foldLeft(leaf())((e, f) => f(e))
+        else os(i) match {
+          case ODefer() => Eval.defer(restart(i + 1, leaf, cbs))
+          case OMemoize() => step(i + 1, leaf, ((e: Eval[A]) => e.memoize) :: cbs)
+          case OMap(f) => step(i + 1, leaf, ((e: Eval[A]) => e.map(f)) :: cbs)
+          case OFlatMap(f) => step(i + 1, leaf, ((e: Eval[A]) => e.flatMap(f)) :: cbs)
+        }
+
+      DeepEval(step(0, leaf, Nil))
+    }
+
+    // we keep this low in master to keep travis happy.
+    // for an actual stress test increase to 200K or so.
+    val MaxDepth = 100
+
+    implicit def arbitraryDeepEval[A: Arbitrary: Cogen]: Arbitrary[DeepEval[A]] = {
+      val gen: Gen[O[A]] = arbitrary[O[A]]
+      Arbitrary(for {
+        leaf <- arbitrary[() => Eval[A]]
+        xs <- Gen.containerOfN[Vector, O[A]](MaxDepth, gen)
+      } yield DeepEval.build(leaf, xs))
+    }
+  }
+
+  // all that work for this one little test.
+
+  test("stack safety stress test") {
+    forAll { (d: DeepEval[Int]) =>
+      try {
+        d.eval.value
+        succeed
+      } catch { case (e: StackOverflowError) =>
+        fail(s"stack overflowed with eval-depth ${DeepEval.MaxDepth}")
+      }
+    }
+  }
+
+  test("memoize handles branched evaluation correctly") {
+    forAll { (e: Eval[Int], fn: Int => Eval[Int]) =>
+      var n0 = 0
+      val a0 = e.flatMap { i => n0 += 1; fn(i); }.memoize
+      assert(a0.flatMap(i1 => a0.map(i1 == _)).value == true)
+      assert(n0 == 1)
+
+      var n1 = 0
+      val a1 = Eval.defer { n1 += 1; fn(0) }.memoize
+      assert(a1.flatMap(i1 => a1.map(i1 == _)).value == true)
+      assert(n1 == 1)
+
+      var n2 = 0
+      val a2 = Eval.defer { n2 += 1; fn(0) }.memoize
+      assert(Eval.defer(a2).value == Eval.defer(a2).value)
+      assert(n2 == 1)
+    }
+  }
 }