diff --git a/src/addition.jl b/src/addition.jl
index 94f8797..ab4cbc0 100644
--- a/src/addition.jl
+++ b/src/addition.jl
@@ -2,7 +2,7 @@
 # between pdmat and pdmat
 
 +(a::PDMat, b::AbstractPDMat) = PDMat(a.mat + Matrix(b))
-+(a::PDiagMat, b::AbstractPDMat) = PDMat(_adddiag!(Matrix(b), a.diag))
++(a::PDiagMat, b::AbstractPDMat) = PDMat(_adddiag!(Matrix(b), a.diag, true))
 +(a::ScalMat, b::AbstractPDMat) = PDMat(_adddiag!(Matrix(b), a.value))
 if HAVE_CHOLMOD
     +(a::PDSparseMat, b::AbstractPDMat) = PDMat(a.mat + Matrix(b))
diff --git a/src/utils.jl b/src/utils.jl
index 3e1453f..c85d938 100644
--- a/src/utils.jl
+++ b/src/utils.jl
@@ -30,7 +30,7 @@ function _adddiag!(a::Union{Matrix, SparseMatrixCSC}, v::Real)
     return a
 end
 
-function _adddiag!(a::Union{Matrix, SparseMatrixCSC}, v::Vector, c::Real)
+function _adddiag!(a::Union{Matrix, SparseMatrixCSC}, v::AbstractVector, c::Real)
     @check_argdims eachindex(v) == axes(a, 1) == axes(a, 2)
     if c == one(c)
         for i in eachindex(v)
@@ -45,8 +45,8 @@ function _adddiag!(a::Union{Matrix, SparseMatrixCSC}, v::Vector, c::Real)
 end
 
 _adddiag(a::Union{Matrix, SparseMatrixCSC}, v::Real) = _adddiag!(copy(a), v)
-_adddiag(a::Union{Matrix, SparseMatrixCSC}, v::Vector, c::Real) = _adddiag!(copy(a), v, c)
-_adddiag(a::Union{Matrix, SparseMatrixCSC}, v::Vector{T}) where {T<:Real} = _adddiag!(copy(a), v, one(T))
+_adddiag(a::Union{Matrix, SparseMatrixCSC}, v::AbstractVector, c::Real) = _adddiag!(copy(a), v, c)
+_adddiag(a::Union{Matrix, SparseMatrixCSC}, v::AbstractVector{T}) where {T<:Real} = _adddiag!(copy(a), v, one(T))
 
 
 function wsumsq(w::AbstractVector, a::AbstractVector)
diff --git a/test/addition.jl b/test/addition.jl
index 9de57f2..32b48e1 100644
--- a/test/addition.jl
+++ b/test/addition.jl
@@ -2,6 +2,18 @@
 
 using PDMats
 
+
+# New AbstractPDMat type for the tests below
+# Supports only functions needed in the tests below
+struct ScalMat3D{T<:Real} <: AbstractPDMat{T}
+    value::T
+end
+Base.Matrix(a::ScalMat3D) = Matrix(Diagonal(fill(a.value, 3)))
+Base.size(::ScalMat3D) = (3, 3)
+# Not generally correct
+Base.:*(a::ScalMat3D, c::Real) = ScalMat3D(a.value * c)
+Base.getindex(a::ScalMat3D, i::Int, j::Int) = i == j ? a.value : zero(a.value)
+
 @testset "addition" begin
     for T in (Float64, Float32)
         printstyled("Testing addition with eltype = $T\n"; color=:blue)
@@ -11,26 +23,35 @@ using PDMats
 
         pm1 = PDMat(M)
         pm2 = PDiagMat(V)
-        pm3 = ScalMat(3, X)
-        pm4 = X * I
+        pm3 = PDiagMat(sparse(V))
+        pm4 = ScalMat(3, X)
         pm5 = PDSparseMat(sparse(M))
+        pm6 = ScalMat3D(X)
 
-        pmats = Any[pm1, pm2, pm3] #, pm5]
+        pmats = Any[pm1, pm2, pm3, pm4, pm5, pm6]
 
         for p1 in pmats, p2 in pmats
             pr = p1 + p2
             @test size(pr) == size(p1)
             @test Matrix(pr) ≈ Matrix(p1) + Matrix(p2)
 
-            pr = pdadd(p1, p2, convert(T, 1.5))
-            @test size(pr) == size(p1)
-            @test Matrix(pr) ≈ Matrix(p1) + Matrix(p2) * convert(T, 1.5)
+            if p1 isa ScalMat3D
+                @test_broken pdadd(p1, p2, convert(T, 1.5))
+            else
+                pr = pdadd(p1, p2, convert(T, 1.5))
+                @test size(pr) == size(p1)
+                @test Matrix(pr) ≈ Matrix(p1) + Matrix(p2) * convert(T, 1.5)
+            end
         end
 
         for p1 in pmats
-            pr = p1 + pm4
-            @test size(pr) == size(p1)
-            @test Matrix(pr) ≈ Matrix(p1) + pm4
+            if p1 isa ScalMat3D
+                @test_broken p1 + X * I
+            else
+                pr = p1 + X * I
+                @test size(pr) == size(p1)
+                @test Matrix(pr) ≈ Matrix(p1) + X * I
+            end
         end
     end
 end