diff --git a/src/prune.jl b/src/prune.jl
index 7f19834..395da7d 100644
--- a/src/prune.jl
+++ b/src/prune.jl
@@ -5,6 +5,7 @@ end
 
 function prune!(solver::SARSOPSolver, tree::SARSOPTree)
     prune!(tree)
+    prune_strictly_dominated!(tree::SARSOPTree)
     if should_prune_alphas(tree)
         prune_alpha!(tree, solver.delta)
     end
@@ -48,60 +49,120 @@ function prune!(tree::SARSOPTree)
     end
 end
 
-function belief_space_domination(α1, α2, B, δ)
-    a1_dominant = true
-    a2_dominant = true
-    for b ∈ B
-        !a1_dominant && !a2_dominant && return (false, false)
-        δV = intersection_distance(α1, α2, b)
-        δV ≤ δ && (a1_dominant = false)
-        δV ≥ -δ && (a2_dominant = false)
-    end
-    return a1_dominant, a2_dominant
-end
-
-@inline function intersection_distance(α1, α2, b)
-    s = 0.0
+function intersection_distance(α1, α2, b)
     dot_sum = 0.0
-    I,B = b.nzind, b.nzval
-    @inbounds for _i ∈ eachindex(I)
+    I, B = b.nzind, b.nzval
+    for _i ∈ eachindex(I)
         i = I[_i]
-        diff = α1[i] - α2[i]
-        s += abs2(diff)
-        dot_sum += diff*B[_i]
+        dot_sum += (α1[i] - α2[i]) * B[_i]
+    end
+    s = 0.0
+    for i ∈ eachindex(α1, α2)
+        s += (α1[i] - α2[i])^2
     end
     return dot_sum / sqrt(s)
 end
 
-function prune_alpha!(tree::SARSOPTree, δ)
+function prune_alpha!(tree::SARSOPTree, δ, eps=0.0)
     Γ = tree.Γ
-    B_valid = tree.b[map(!,tree.b_pruned)]
-    pruned = falses(length(Γ))
-
-    # checking if α_i dominates α_j
-    for (i,α_i) ∈ enumerate(Γ)
-        pruned[i] && continue
-        for (j,α_j) ∈ enumerate(Γ)
-            (j ≤ i || pruned[j]) && continue
-            a1_dominant,a2_dominant = belief_space_domination(α_i, α_j, B_valid, δ)
-            #=
-            NOTE: α1 and α2 shouldn't technically be able to mutually dominate
-            i.e. a1_dominant and a2_dominant should never both be true.
-            But this does happen when α1 == α2 because intersection_distance returns NaN.
-            Current impl prunes α2 without doing an equality check, removing
-            the duplicate α. Could do equality check to short-circuit
-            belief_space_domination which would speed things up if we have
-            a lot of duplicates, but the equality check can slow things down
-            if α's are sufficiently diverse.
-            =#
-            if a1_dominant
-                pruned[j] = true
-            elseif a2_dominant
-                pruned[i] = true
-                break
+    B_valid = tree.b[map(!, tree.b_pruned)]
+
+    n_Γ = length(Γ)
+    n_B = length(B_valid)
+
+    dominant_indices_bools = falses(n_Γ)
+    dominant_vector_indices = Vector{Int}(undef, n_B)
+
+    # First, identify dominant alpha vectors
+    for b_idx in 1:n_B
+        max_value = -Inf
+        max_index = -1
+        for i in 1:n_Γ
+            value = dot(Γ[i], B_valid[b_idx])
+            if value > max_value
+                max_value = value
+                max_index = i
             end
         end
+        dominant_indices_bools[max_index] = true
+        dominant_vector_indices[b_idx] = max_index
     end
-    deleteat!(Γ, pruned)
+
+    non_dominant_indices = findall(!, dominant_indices_bools)
+    n_non_dom = length(non_dominant_indices)
+    keep_non_dom = falses(n_non_dom)
+
+    for b_idx in 1:n_B
+        dom_vec_idx = dominant_vector_indices[b_idx]
+        for j in 1:n_non_dom
+            non_dom_idx = non_dominant_indices[j]
+            if keep_non_dom[j]
+                continue
+            end
+            intx_dist = intersection_distance(Γ[dom_vec_idx], Γ[non_dom_idx], B_valid[b_idx])
+            if !isnan(intx_dist) && (intx_dist + eps ≤ δ)
+                keep_non_dom[j] = true
+            end
+        end
+    end
+
+    non_dominant_indices = non_dominant_indices[.!keep_non_dom]
+    deleteat!(Γ, non_dominant_indices)
     tree.prune_data.last_Γ_size = length(Γ)
 end
+
+function strictly_dominates(α1, α2, eps)
+    for ii in 1:length(α1)
+        if α1[ii] < α2[ii] - eps
+            return false
+        end
+    end
+    return true
+end
+
+function prune_strictly_dominated!(tree::SARSOPTree, eps=1e-10)
+    Γ = tree.Γ
+    Γ_new_idxs = Vector{Int}(undef, length(Γ))
+    keep = trues(length(Γ))
+
+    idx_count = 0
+    for (α_try_idx, α_try) in enumerate(Γ)
+        dominated = false
+        for jj in 1:idx_count
+            α_in_idx = Γ_new_idxs[jj]
+            α_in = Γ[α_in_idx]
+            if strictly_dominates(α_try, α_in, eps)
+                keep[jj] = false
+            elseif strictly_dominates(α_in, α_try, eps)
+                dominated = true
+                break
+            end
+        end
+        if !dominated
+            new_idx_count = 0
+            for jj in 1:idx_count
+                if keep[jj]
+                    new_idx_count += 1
+                    Γ_new_idxs[new_idx_count] = Γ_new_idxs[jj]
+                end
+            end
+            new_idx_count += 1
+            Γ_new_idxs[new_idx_count] = α_try_idx
+            idx_count = new_idx_count
+            fill!(keep, true)
+        end
+    end
+
+    resize!(Γ_new_idxs, idx_count)
+
+    to_delete = trues(length(Γ))
+    for idx in Γ_new_idxs
+        to_delete[idx] = false
+    end
+
+    for ii in length(Γ):-1:1
+        if to_delete[ii]
+            deleteat!(Γ, ii)
+        end
+    end
+end
diff --git a/test/prune.jl b/test/prune.jl
new file mode 100644
index 0000000..f55fb36
--- /dev/null
+++ b/test/prune.jl
@@ -0,0 +1,19 @@
+@testset "prune" begin
+    # NativeSARSOP.strictly_dominates
+    a1 = [1.0, 2.0, 3.0]
+    a2 = [1.0, 2.1, 2.9]
+    a3 = [0.9, 1.9, 2.9]
+    @test !NativeSARSOP.strictly_dominates(a1, a2, 1e-10)
+    @test NativeSARSOP.strictly_dominates(a1, a1, 1e-10)
+    @test NativeSARSOP.strictly_dominates(a1, a3, 1e-10)
+
+    # NativeSARSOP.intersection_distance
+    b = SparseVector([1.0, 0.0])
+    a1 = [1.0, 0.0]
+    a2 = [0.0, 1.0]
+    @test isapprox(NativeSARSOP.intersection_distance(a1, a2, b),
+        sqrt(0.5^2 + 0.5^2), atol=1e-10)
+
+    b = SparseVector([0.5, 0.5])
+    @test isapprox(NativeSARSOP.intersection_distance(a1, a2, b), 0.0, atol=1e-10)
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 806fca1..044dfde 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -27,6 +27,8 @@ include("sample.jl")
 
 include("updater.jl")
 
+include("prune.jl")
+
 include("tree.jl")
 
 @testset "Tiger POMDP" begin