diff --git a/src/SDiagonal.jl b/src/SDiagonal.jl
index d1e92caa..d726eaba 100644
--- a/src/SDiagonal.jl
+++ b/src/SDiagonal.jl
@@ -17,6 +17,10 @@ SDiagonal(a::StaticMatrix{N,N,T}) where {N,T} = Diagonal(diag(a))
 size(::Type{<:SDiagonal{N}}) where {N} = (N,N)
 size(::Type{<:SDiagonal{N}}, d::Int) where {N} = d > 2 ? 1 : N
 
+Base.axes(D::SDiagonal, d) = d <= 2 ? axes(D)[d] : SOneTo(1)
+
+Base.reshape(a::SDiagonal, s::Tuple{SOneTo,Vararg{SOneTo}}) = reshape(a, homogenize_shape(s))
+
 # define specific methods to avoid allocating mutable arrays
 \(D::SDiagonal, b::AbstractVector) = D.diag .\ b
 \(D::SDiagonal, b::StaticVector) = D.diag .\ b # catch ambiguity
@@ -56,3 +60,5 @@ function inv(D::SDiagonal)
     check_singular(D)
     SDiagonal(inv.(D.diag))
 end
+
+Base.copy(D::SDiagonal) = Diagonal(copy(diag(D)))
diff --git a/src/indexing.jl b/src/indexing.jl
index dffb0cef..98315e4d 100644
--- a/src/indexing.jl
+++ b/src/indexing.jl
@@ -377,3 +377,21 @@ Base.unsafe_view(A::AbstractArray, i1::StaticIndexing, indices::StaticIndexing..
 # the tuple indices has to have at least one element to prevent infinite
 # recursion when viewing a zero-dimensional array (see issue #705)
 Base.SubArray(A::AbstractArray, indices::Tuple{StaticIndexing, Vararg{StaticIndexing}}) = Base.SubArray(A, map(unwrap, indices))
+
+###########################################################
+# SDiagonal
+###########################################################
+
+# SDiagonal uses Cartesian indexing, and the canonical indexing methods shadow getindex for Diagonal
+# these are needed for ambiguity resolution
+@inline function getindex(D::SDiagonal, i::Int, j::Int)
+    invoke(getindex, Tuple{Diagonal, Int, Int}, D, i, j)
+end
+@inline function getindex(D::SDiagonal, i::Int...)
+    invoke(getindex, Tuple{Diagonal, Vararg{Int}}, D, i...)
+end
+# Ensure that vector indexing with static types lead to SArrays
+@propagate_inbounds function getindex(a::SDiagonal, inds::Union{Int, StaticArray{<:Tuple, Int}, SOneTo, Colon}...)
+    ar = reshape(a, Val(length(inds)))
+    _getindex(ar, index_sizes(Size(ar), inds...), inds)
+end
diff --git a/test/SDiagonal.jl b/test/SDiagonal.jl
index ff94f849..7d1090c6 100644
--- a/test/SDiagonal.jl
+++ b/test/SDiagonal.jl
@@ -70,6 +70,15 @@ using StaticArrays, Test, LinearAlgebra
 
         @test length(m) === 4*4
 
+        m2 = SMatrix{4,4}(m)
+        @test (@inferred axes(m)) === axes(m2)
+        @test axes(m, 1) === axes(m2, 1)
+        @test axes(m, 3) == SOneTo(1)
+
+        @test m[:, 1] === SVector{4}(m[1,1], 0, 0, 0)
+        @test m[:, :] === m2
+        @test m[2, 2, 1] === m[2, 2]
+
         @test_throws Exception m[1] = 1
 
         b = @SVector [2,-1,2,1]
@@ -114,5 +123,7 @@ using StaticArrays, Test, LinearAlgebra
 
         @test m + zero(m) == m
         @test m + zero(typeof(m)) == m
+
+        @test copy(m) === m
     end
 end