diff --git a/src/WoodburyMatrices.jl b/src/WoodburyMatrices.jl
index 0300ee2..b4965eb 100644
--- a/src/WoodburyMatrices.jl
+++ b/src/WoodburyMatrices.jl
@@ -98,10 +98,23 @@ _ldiv!(dest, W, A, B) = _ldiv!(dest, W, defaultfactor(W, A), B)
 
 defaultfactor(::AbstractWoodbury, A) = lu(A)
 
-det(W::AbstractWoodbury) = det(W.A)*det(W.C)/det(W.Cp)
-logdet(W::AbstractWoodbury) = logdet(W.A) + logdet(W.C) - logdet(W.Cp)
+function det(W::AbstractWoodbury)
+    ret = det(W.A)
+    if !isempty(W.C)
+        ret *= det(W.C)/det(W.Cp)
+    end
+    return ret
+end
+function logdet(W::AbstractWoodbury)
+    ret = logdet(W.A)
+    if !isempty(W.C)
+        ret += logdet(W.C) - logdet(W.Cp)
+    end
+    return ret
+end
 function logabsdet(W::AbstractWoodbury)
     lad_A = logabsdet(W.A)
+    isempty(W.C) && return lad_A
     lad_C = logabsdet(W.C)
     lad_Cp = logabsdet(W.Cp)
     lad = lad_A[1] + lad_C[1] - lad_Cp[1]
diff --git a/test/symwoodbury.jl b/test/symwoodbury.jl
index 0706f3c..ae76fef 100644
--- a/test/symwoodbury.jl
+++ b/test/symwoodbury.jl
@@ -226,4 +226,16 @@ W = SymWoodbury([randpsd(50) for _ in 1:3]...)
     @test W \ [13, 14, 15, 16] ≈ Matrix(W) \ [13, 14, 15, 16]
 end
 
+@testset "Empty B" begin
+    A = Diagonal( Float64[1,2,3,4] )
+    B = Matrix{Float64}(undef, 4, 0)
+    D = Diagonal(Float64[])
+
+    W = SymWoodbury( A, B, D)
+    @test W \ [13, 14, 15, 16] ≈ Matrix(W) \ [13, 14, 15, 16]
+    @test det(W) ≈ det(Matrix(W))
+    @test logdet(W) ≈ logdet(Matrix(W))
+    @test all(logabsdet(W) .≈ logabsdet(Matrix(W)))
+end
+
 end # @testset "SymWoodbury"
diff --git a/test/woodbury.jl b/test/woodbury.jl
index 8fd49fc..eeea2ee 100644
--- a/test/woodbury.jl
+++ b/test/woodbury.jl
@@ -184,4 +184,16 @@ W = Woodbury([randpsd(50) for _ in 1:4]...)
 @test logdet(W) ≈ log(det(W)) ≈ logdet(Array(W))
 @test all(logabsdet(W) .≈ logabsdet(Array(W)))
 
+@testset "Empty U" begin
+    A = Diagonal( Float64[1,2,3,4] )
+    B = Matrix{Float64}(undef, 4, 0)
+    D = Diagonal(Float64[])
+
+    W = Woodbury( A, B, D, B')
+    @test W \ [13, 14, 15, 16] ≈ Matrix(W) \ [13, 14, 15, 16]
+    @test det(W) ≈ det(Matrix(W))
+    @test logdet(W) ≈ logdet(Matrix(W))
+    @test all(logabsdet(W) .≈ logabsdet(Matrix(W)))
+end
+
 end  # @testset "Woodbury"