diff --git a/src/valuations.jl b/src/valuations.jl
index c858dff..ebdf728 100644
--- a/src/valuations.jl
+++ b/src/valuations.jl
@@ -50,7 +50,7 @@ Get the domain of ``\\phi``.
 domain(ϕ::Valuation)
 
 function domain(ϕ::IdentityValuation{T}) where T
-    Set{T}()
+    T[]
 end
 
 function domain(ϕ::LabeledBox)
@@ -135,6 +135,7 @@ function project(ϕ::LabeledBox, x)
 end
 
 function project(ϕ::LabeledBox{<:Any, <:GaussianSystem}, x)
+    @assert x ⊆ ϕ.labels
     m = [X in x for X in ϕ.labels]
     LabeledBox(ϕ.labels[m], marginal(m, ϕ.box))
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 402c67a..35d6e14 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -87,28 +87,57 @@ using Test
         :measure => kernel(R, H),
         :observe₁ => normal(z₁),
         :observe₂ => normal(z₂))
+
     Σ = oapply(composite, box_map)
     @test isapprox(true_cov, cov(Σ); rtol=1e-3)
     @test isapprox(true_mean, mean(Σ); rtol=1e-3)
 
     kb, query = inference_problem(composite, box_map)
+    @test query == Set([:x21, :x22, :x23, :x24, :x25, :x26])
+
     jt = architecture(kb, minfill!(primal_graph(kb), query))
+    @test_throws ErrorException("Query not covered by join tree.") answer_query(jt, [:x31])
+    @test_throws ErrorException("Query not covered by join tree.") answer_query!(jt, [:x31])
+
     ϕ = answer_query(jt, query)
     M = [i == j for i in [:x21, :x22, :x23, :x24, :x25, :x26], j in ϕ.labels]
+    @test length(ϕ) == length(query)
     @test Set(domain(ϕ)) == query
     @test isapprox(true_cov, M * cov(ϕ.box) * M'; rtol=1e-3)
     @test isapprox(true_mean, M * mean(ϕ.box); rtol=1e-3)
 
-    jt = architecture(kb, minwidth!(primal_graph(kb), query))
+    ϕ = answer_query!(jt, query)
+    M = [i == j for i in [:x21, :x22, :x23, :x24, :x25, :x26], j in ϕ.labels]
+    @test length(ϕ) == length(query)
+    @test Set(domain(ϕ)) == query
+    @test isapprox(true_cov, M * cov(ϕ.box) * M'; rtol=1e-3)
+    @test isapprox(true_mean, M * mean(ϕ.box); rtol=1e-3)
+
+    jt = architecture(kb, minwidth!(primal_graph(kb), []))
+
     ϕ = answer_query(jt, query)
     M = [i == j for i in [:x21, :x22, :x23, :x24, :x25, :x26], j in ϕ.labels]
+    @test length(ϕ) == length(query)
     @test Set(domain(ϕ)) == query
     @test isapprox(true_cov, M * cov(ϕ.box) * M'; rtol=1e-3)
     @test isapprox(true_mean, M * mean(ϕ.box); rtol=1e-3)
 
     ϕ = answer_query!(jt, query)
     M = [i == j for i in [:x21, :x22, :x23, :x24, :x25, :x26], j in ϕ.labels]
+    @test length(ϕ) == length(query)
     @test Set(domain(ϕ)) == query
     @test isapprox(true_cov, M * cov(ϕ.box) * M'; rtol=1e-3)
     @test isapprox(true_mean, M * mean(ϕ.box); rtol=1e-3)
 end
+
+@testset "Identity Valuation" begin
+    ϕ = LabeledBox([:x, :y], normal([1 0; 0 1]))
+    e = IdentityValuation{Symbol}()
+
+    @test isempty(domain(e))
+    @test eltype(domain(e)) == Symbol
+    @test combine(e, e) === e
+    @test combine(ϕ, e) === ϕ
+    @test combine(e, ϕ) === ϕ
+    @test project(e, []) === e
+end