diff --git a/packages/squiggle-lang/__tests__/Distributions/KlDivergence_test.res b/packages/squiggle-lang/__tests__/Distributions/KlDivergence_test.res
index bb21ba7f..2ba5100e 100644
--- a/packages/squiggle-lang/__tests__/Distributions/KlDivergence_test.res
+++ b/packages/squiggle-lang/__tests__/Distributions/KlDivergence_test.res
@@ -19,7 +19,7 @@ describe("kl divergence on continuous distributions", () => {
       let analyticalKl = Js.Math.log((highPrediction -. lowPrediction) /. (highAnswer -. lowAnswer))
       let kl = E.R.liftJoin2(klDivergence, prediction, answer)
       switch kl {
-      | Ok(kl') => kl'->expect->toBeCloseTo(analyticalKl)
+      | Ok(kl') => kl'->expect->toBeSoCloseTo(analyticalKl, ~digits=7)
       | Error(err) => {
           Js.Console.log(DistributionTypes.Error.toString(err))
           raise(KlFailed)
@@ -51,7 +51,7 @@ describe("kl divergence on continuous distributions", () => {
     let kl = E.R.liftJoin2(klDivergence, prediction, answer)
 
     switch kl {
-    | Ok(kl') => kl'->expect->toBeCloseTo(analyticalKl)
+    | Ok(kl') => kl'->expect->toBeSoCloseTo(analyticalKl, ~digits=3)
     | Error(err) => {
         Js.Console.log(DistributionTypes.Error.toString(err))
         raise(KlFailed)
@@ -78,9 +78,9 @@ describe("kl divergence on discrete distributions", () => {
     | (Dist(prediction'), Dist(answer')) => klDivergence(prediction', answer')
     | _ => raise(MixtureFailed)
     }
-    let analyticalKl = Js.Math.log(2.0 /. 3.0)
+    let analyticalKl = Js.Math.log(3.0 /. 2.0)
     switch kl {
-    | Ok(kl') => kl'->expect->toBeCloseTo(analyticalKl)
+    | Ok(kl') => kl'->expect->toBeSoCloseTo(analyticalKl, ~digits=7)
     | Error(err) =>
       Js.Console.log(DistributionTypes.Error.toString(err))
       raise(KlFailed)
diff --git a/packages/squiggle-lang/__tests__/TestHelpers.res b/packages/squiggle-lang/__tests__/TestHelpers.res
index 54c4c814..21f3c51c 100644
--- a/packages/squiggle-lang/__tests__/TestHelpers.res
+++ b/packages/squiggle-lang/__tests__/TestHelpers.res
@@ -51,6 +51,7 @@ let mkExponential = rate => DistributionTypes.Symbolic(#Exponential({rate: rate}
 let mkUniform = (low, high) => DistributionTypes.Symbolic(#Uniform({low: low, high: high}))
 let mkCauchy = (local, scale) => DistributionTypes.Symbolic(#Cauchy({local: local, scale: scale}))
 let mkLognormal = (mu, sigma) => DistributionTypes.Symbolic(#Lognormal({mu: mu, sigma: sigma}))
+let mkDirac = x => DistributionTypes.Symbolic(#Float(x))
 
 let normalMake = SymbolicDist.Normal.make
 let betaMake = SymbolicDist.Beta.make
diff --git a/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Discrete.res b/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Discrete.res
index 31694232..658b7dc9 100644
--- a/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Discrete.res
+++ b/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/Discrete.res
@@ -229,11 +229,25 @@ module T = Dist({
   }
 
   let klDivergence = (prediction: t, answer: t) => {
-    combinePointwise(
-      ~combiner=XYShape.PointwiseCombination.combineAlongSupportOfSecondArgument0,
-      ~fn=PointSetDist_Scoring.KLDivergence.integrand,
-      prediction,
-      answer,
-    ) |> E.R2.bind(integralEndYResult)
+    let massOrZero = (t: t, x: float): float => {
+      let i = E.A.findIndex(x' => x' == x, t.xyShape.xs)
+      switch i {
+      | None => 0.0
+      | Some(i') => t.xyShape.ys[i']
+      }
+    }
+    let predictionNewYs = E.A.fmap(massOrZero(answer), prediction.xyShape.xs)
+    let integrand = XYShape.PointwiseCombination.combine(
+      PointSetDist_Scoring.KLDivergence.integrand,
+      XYShape.XtoY.continuousInterpolator(#Stepwise, #UseZero),
+      {XYShape.xs: answer.xyShape.xs, XYShape.ys: predictionNewYs},
+      answer.xyShape,
+    )
+    let xyShapeToDiscrete: XYShape.xyShape => t = xyShape => {
+      xyShape: xyShape,
+      integralSumCache: None,
+      integralCache: None,
+    }
+    integrand->E.R2.fmap(x => x->xyShapeToDiscrete->integralEndY)
   }
 })
diff --git a/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/PointSetDist.res b/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/PointSetDist.res
index 0a8d2987..1879ebdd 100644
--- a/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/PointSetDist.res
+++ b/packages/squiggle-lang/src/rescript/Distributions/PointSetDist/PointSetDist.res
@@ -199,6 +199,7 @@ module T = Dist({
   let klDivergence = (t1: t, t2: t) =>
     switch (t1, t2) {
     | (Continuous(t1), Continuous(t2)) => Continuous.T.klDivergence(t1, t2)
+    | (Discrete(t1), Discrete(t2)) => Discrete.T.klDivergence(t1, t2)
     | _ => Error(NotYetImplemented)
     }
 })