diff --git a/src/main/kotlin/org/wfanet/measurement/measurementconsumer/stats/Variances.kt b/src/main/kotlin/org/wfanet/measurement/measurementconsumer/stats/Variances.kt
index 1e79b28ee9d..c5d4b8576db 100644
--- a/src/main/kotlin/org/wfanet/measurement/measurementconsumer/stats/Variances.kt
+++ b/src/main/kotlin/org/wfanet/measurement/measurementconsumer/stats/Variances.kt
@@ -161,7 +161,7 @@ object VariancesImpl : Variances {
       multiplier: Int) =
       relativeFrequencyMeasurementVarianceParams
 
-    require(totalReach > 0) { "Total reach must be positive, but got $totalReach." }
+    require(totalReach >= 0) { "Total reach must be non-negative, but got $totalReach." }
     require(reachRatio >= 0.0 && reachRatio <= 1.0) {
       "Reach ratio must be greater than or equal to 0 and less than or equal to 1, but got " +
         "$reachRatio."
@@ -199,7 +199,7 @@ object VariancesImpl : Variances {
     reachRatio: Double,
     reachRatioVariance: Double,
   ): Double {
-    require(totalReach > 0) { "Total reach must be positive, but got $totalReach." }
+    require(totalReach >= 0) { "Total reach must be non-negative, but got $totalReach." }
     require(totalReachVariance >= 0) {
       "Total reach variance must not be negative, but got $totalReachVariance."
     }
diff --git a/src/test/kotlin/org/wfanet/measurement/measurementconsumer/stats/VariancesTest.kt b/src/test/kotlin/org/wfanet/measurement/measurementconsumer/stats/VariancesTest.kt
index e7ef79b7aa8..e202451d63f 100644
--- a/src/test/kotlin/org/wfanet/measurement/measurementconsumer/stats/VariancesTest.kt
+++ b/src/test/kotlin/org/wfanet/measurement/measurementconsumer/stats/VariancesTest.kt
@@ -2548,6 +2548,211 @@ class VariancesTest {
       .of(expectedNKPlus)
   }
 
+  @Test
+  fun `computeMeasurementVariance returns for deterministic reach-frequency when total reach is zero and zero relative frequencies `() {
+    val vidSamplingIntervalWidth = 5e-2
+    val totalReach = 0L
+    val reachDpParams = DpParams(0.5, 1e-15)
+    val reachMeasurementParams =
+      ReachMeasurementParams(
+        VidSamplingInterval(0.0, vidSamplingIntervalWidth),
+        reachDpParams,
+        NoiseMechanism.GAUSSIAN,
+      )
+    val reachMeasurementVarianceParams =
+      ReachMeasurementVarianceParams(totalReach, reachMeasurementParams)
+    val reachMeasurementVariance =
+      VariancesImpl.computeMeasurementVariance(
+        DeterministicMethodology,
+        reachMeasurementVarianceParams,
+      )
+
+    val maximumFrequency = 5
+    val relativeFrequencyDistribution = (1..maximumFrequency).associateWith { 0.0 }
+    val frequencyDpParams = DpParams(0.2, 1e-15)
+    val frequencyMeasurementParams =
+      FrequencyMeasurementParams(
+        VidSamplingInterval(0.0, vidSamplingIntervalWidth),
+        frequencyDpParams,
+        NoiseMechanism.GAUSSIAN,
+        maximumFrequency,
+      )
+    val frequencyMeasurementVarianceParams =
+      FrequencyMeasurementVarianceParams(
+        totalReach,
+        reachMeasurementVariance,
+        relativeFrequencyDistribution,
+        frequencyMeasurementParams,
+      )
+
+    val (rKVars, rKPlusVars, nKVars, nKPlusVars) =
+      VariancesImpl.computeMeasurementVariance(
+        DeterministicMethodology,
+        frequencyMeasurementVarianceParams,
+      )
+
+    val expectedRK =
+      listOf(
+        0.08333333333333336,
+        0.08333333333333336,
+        0.08333333333333336,
+        0.08333333333333336,
+        0.08333333333333336,
+      )
+    val expectedRKPlus =
+      listOf(
+        0.0,
+        0.08333333333333336,
+        0.08333333333333336,
+        0.08333333333333336,
+        0.08333333333333336,
+      )
+    val expectedNK =
+      listOf(
+        7244.988593451251,
+        7244.988593451251,
+        7244.988593451251,
+        7244.988593451251,
+        7244.988593451251,
+      )
+    val expectedNKPlus =
+      listOf(0.0, 7244.988593451251, 7244.988593451251, 7244.988593451251, 7244.988593451251)
+
+    for (frequency in 1..maximumFrequency) {
+      assertThat(rKVars.getValue(frequency))
+        .isWithin(computeErrorTolerance(rKVars.getValue(frequency), expectedRK[frequency - 1]))
+        .of(expectedRK[frequency - 1])
+    }
+    for (frequency in 1..maximumFrequency) {
+      assertThat(rKPlusVars.getValue(frequency))
+        .isWithin(
+          computeErrorTolerance(rKPlusVars.getValue(frequency), expectedRKPlus[frequency - 1])
+        )
+        .of(expectedRKPlus[frequency - 1])
+    }
+    for (frequency in 1..maximumFrequency) {
+      assertThat(nKVars.getValue(frequency))
+        .isWithin(computeErrorTolerance(nKVars.getValue(frequency), expectedNK[frequency - 1]))
+        .of(expectedNK[frequency - 1])
+    }
+    for (frequency in 1..maximumFrequency) {
+      assertThat(nKPlusVars.getValue(frequency))
+        .isWithin(
+          computeErrorTolerance(nKPlusVars.getValue(frequency), expectedNKPlus[frequency - 1])
+        )
+        .of(expectedNKPlus[frequency - 1])
+    }
+  }
+
+  @Test
+  fun `computeMeasurementVariance returns for deterministic reach-frequency when total reach is zero and regular relative frequencies `() {
+    val vidSamplingIntervalWidth = 5e-2
+    val totalReach = 0L
+    val reachDpParams = DpParams(0.5, 1e-15)
+    val reachMeasurementParams =
+      ReachMeasurementParams(
+        VidSamplingInterval(0.0, vidSamplingIntervalWidth),
+        reachDpParams,
+        NoiseMechanism.GAUSSIAN,
+      )
+    val reachMeasurementVarianceParams =
+      ReachMeasurementVarianceParams(totalReach, reachMeasurementParams)
+    val reachMeasurementVariance =
+      VariancesImpl.computeMeasurementVariance(
+        DeterministicMethodology,
+        reachMeasurementVarianceParams,
+      )
+
+    val maximumFrequency = 5
+    val relativeFrequencyDistribution =
+      mapOf(
+        1 to 0.4351145038167939,
+        2 to 0.0,
+        3 to 0.3816793893129771,
+        4 to 0.1832061068702290,
+        5 to 0.0,
+      )
+    val frequencyDpParams = DpParams(0.2, 1e-15)
+    val frequencyMeasurementParams =
+      FrequencyMeasurementParams(
+        VidSamplingInterval(0.0, vidSamplingIntervalWidth),
+        frequencyDpParams,
+        NoiseMechanism.GAUSSIAN,
+        maximumFrequency,
+      )
+    val frequencyMeasurementVarianceParams =
+      FrequencyMeasurementVarianceParams(
+        totalReach,
+        reachMeasurementVariance,
+        relativeFrequencyDistribution,
+        frequencyMeasurementParams,
+      )
+
+    val (rKVars, rKPlusVars, nKVars, nKPlusVars) =
+      VariancesImpl.computeMeasurementVariance(
+        DeterministicMethodology,
+        frequencyMeasurementVarianceParams,
+      )
+
+    val expectedRK =
+      listOf(
+        0.08333333333333336,
+        0.08333333333333336,
+        0.08333333333333336,
+        0.08333333333333336,
+        0.08333333333333336,
+      )
+    val expectedRKPlus =
+      listOf(
+        0.0,
+        0.08333333333333336,
+        0.08333333333333336,
+        0.08333333333333336,
+        0.08333333333333336,
+      )
+    val expectedNK =
+      listOf(
+        23699.39297634332,
+        7243.321926784585,
+        19905.73424562018,
+        10160.74172504431,
+        7243.321926784585,
+      )
+    val expectedNKPlus =
+      listOf(
+        86919.86312141502,
+        34979.06986996207,
+        34979.06986996207,
+        10160.74172504431,
+        7243.321926784585,
+      )
+
+    for (frequency in 1..maximumFrequency) {
+      assertThat(rKVars.getValue(frequency))
+        .isWithin(computeErrorTolerance(rKVars.getValue(frequency), expectedRK[frequency - 1]))
+        .of(expectedRK[frequency - 1])
+    }
+    for (frequency in 1..maximumFrequency) {
+      assertThat(rKPlusVars.getValue(frequency))
+        .isWithin(
+          computeErrorTolerance(rKPlusVars.getValue(frequency), expectedRKPlus[frequency - 1])
+        )
+        .of(expectedRKPlus[frequency - 1])
+    }
+    for (frequency in 1..maximumFrequency) {
+      assertThat(nKVars.getValue(frequency))
+        .isWithin(computeErrorTolerance(nKVars.getValue(frequency), expectedNK[frequency - 1]))
+        .of(expectedNK[frequency - 1])
+    }
+    for (frequency in 1..maximumFrequency) {
+      assertThat(nKPlusVars.getValue(frequency))
+        .isWithin(
+          computeErrorTolerance(nKPlusVars.getValue(frequency), expectedNKPlus[frequency - 1])
+        )
+        .of(expectedNKPlus[frequency - 1])
+    }
+  }
+
   @Test
   fun `computeMeasurementVariance returns for LiquidLegionsSketch reach-frequency when reach is too small`() {
     val decayRate = 100.0