diff --git a/src/explorers/SliceSampler.jl b/src/explorers/SliceSampler.jl
index 1a940e732..43622c3b5 100644
--- a/src/explorers/SliceSampler.jl
+++ b/src/explorers/SliceSampler.jl
@@ -166,6 +166,11 @@ function slice_shrink!(h::SliceSampler, replica, z, L, R, lp_L, lp_R, pointer, l
         else
             Rbar = new_position
         end
+        if Lbar ≈ Rbar 
+            # see https://github.com/UBC-Stat-ML/blangSDK/blob/b8642c9c2a0adab8a5b6da96f2a7889f1b81b6cc/src/main/java/blang/mcmc/RealSliceSampler.java#L111
+            pointer[] = old_position 
+            return log_potential(state) 
+        end
         n += 1
     end
     # code should never get here, because eventually
diff --git a/test/test_slice_sampler.jl b/test/test_slice_sampler.jl
index 274a0d2b2..be84a1dc0 100644
--- a/test/test_slice_sampler.jl
+++ b/test/test_slice_sampler.jl
@@ -117,4 +117,19 @@ end
                 explorer = SliceSampler(w = 0.1, p = 20, n_passes = 1, max_iter = 1_024)
                 )
     @test_throws "AssertionError: for integer variables, the width should be an integer. Got: 0.1" pt = pigeons(inputs)
+end
+
+# This covers the Lbar ≈ Rbar check in slice_shrink!
+struct Dirac end 
+function (::Dirac)(x) # Dirac in first coordinate, Gaussian in the second
+    return x[1] == 1.1 ? -x[2]^2/2.0 : -Inf64  
+end
+Pigeons.initialization(::Dirac, ::AbstractRNG, ::Int) = [1.1, 0.0] 
+
+@testset "Dirac" begin 
+    pt = pigeons(target = Dirac(), reference = Dirac(), n_chains = 1, record = [online], n_rounds = 15)
+    @test mean(pt)[1] == 1.1 
+    @test ≈(mean(pt)[2], 0.0, atol = 0.01) 
+    @test var(pt)[1] == 0.0 
+    @test ≈(var(pt)[2], 1.0, atol = 0.01)
 end
\ No newline at end of file