diff --git a/src/mapreduce.jl b/src/mapreduce.jl
index 202dddf7..0b747e0b 100644
--- a/src/mapreduce.jl
+++ b/src/mapreduce.jl
@@ -158,6 +158,9 @@ end
     end
 end
 
+@inline _mapreduce(f, op, D::Tuple{<:Any}, init, sz::Size{S}, a::StaticArray) where {S} =
+    _mapreduce(f, op, first(D), init, sz, a)
+
 @generated function _mapfoldl(f, op, dims::Val{D}, init,
                                ::Size{S}, a::StaticArray) where {S,D}
     N = length(S)
@@ -209,6 +212,14 @@ reduce(::typeof(hcat), A::StaticArray{<:Tuple,<:StaticVecOrMatLike}) =
 @inline _reduce(op, a::StaticArray, dims, init = _InitialValue()) =
     _mapreduce(identity, op, dims, init, Size(a), a)
 
+@inline function _reduce(op, a::StaticArray, dims::Tuple, init = _InitialValue())
+    b = _reduce(op, a, first(dims))
+    return _reduce(op, b, Base.tail(dims), init)
+end
+_reduce(op, a::StaticArray, dims::Tuple{}, ::_InitialValue) = a
+_reduce(op, a::StaticArray, dims::Tuple{}, init) = op.(init, a)
+
+
 ################
 ## (map)foldl ##
 ################
diff --git a/test/mapreduce.jl b/test/mapreduce.jl
index 5c7c78ca..9cacc21a 100644
--- a/test/mapreduce.jl
+++ b/test/mapreduce.jl
@@ -37,9 +37,12 @@ using Statistics: mean
         v2 = [4,3,2,1]; sv2 = SVector{4}(v2)
         @test reduce(+, sv1) === reduce(+, v1)
         @test reduce(+, sv1; init=0) === reduce(+, v1; init=0)
+        @test reduce(+, sv1; init=99) === reduce(+, v1; init=99)
         @test reduce(max, sa; dims=Val(1), init=-1.) === SMatrix{1,J}(reduce(max, a, dims=1, init=-1.))
         @test reduce(max, sa; dims=1, init=-1.) === SMatrix{1,J}(reduce(max, a, dims=1, init=-1.))
         @test reduce(max, sa; dims=2, init=-1.) === SMatrix{I,1}(reduce(max, a, dims=2, init=-1.))
+        @test reduce(*, sa; dims=(1,2), init=2.0) ≈ SMatrix{1,1}(reduce(*, a, dims=(1,2), init=2.0))
+        @test reduce(*, sa; dims=(), init=(1.0+im)) === SMatrix{I,J}(reduce(*, a, dims=(), init=(1.0+im)))
         @test mapreduce(-, +, sv1) === mapreduce(-, +, v1)
         @test mapreduce(-, +, sv1; init=0) === mapreduce(-, +, v1, init=0)
         @test mapreduce(*, +, sv1, sv2) === 40
@@ -47,6 +50,11 @@ using Statistics: mean
         @test mapreduce(x->x^2, max, sa; dims=Val(1), init=-1.) == SMatrix{1,J}(mapreduce(x->x^2, max, a, dims=1, init=-1.))
         @test mapreduce(x->x^2, max, sa; dims=1, init=-1.) == SMatrix{1,J}(mapreduce(x->x^2, max, a, dims=1, init=-1.))
         @test mapreduce(x->x^2, max, sa; dims=2, init=-1.) == SMatrix{I,1}(mapreduce(x->x^2, max, a, dims=2, init=-1.))
+
+        # Zero-dim array
+        a0 = fill(rand()); sa0 = SArray{Tuple{}}(a0)
+        @test reduce(+, sa0) === reduce(+, a0)
+        @test reduce(/, sa0, dims=(), init=1.2) === SArray{Tuple{}}(reduce(/, a0, dims=(), init=1.2))
     end
 
     @testset "[map]foldl" begin
@@ -102,6 +110,7 @@ using Statistics: mean
         RSArray1 = SArray{Tuple{1,J,K}}  # reduced in dimension 1
         RSArray2 = SArray{Tuple{I,1,K}}  # reduced in dimension 2
         RSArray3 = SArray{Tuple{I,J,1}}  # reduced in dimension 3
+        RSArray13 = SArray{Tuple{1,J,1}}  # reduced in dimension 1 and 3
         a = randn(I,J,K); sa = OSArray(a)
         b = rand(Bool,I,J,K); sb = OSArray(b)
         z = zeros(I,J,K); sz = OSArray(z)
@@ -111,8 +120,11 @@ using Statistics: mean
         @test sum(sa) === sum(a)
         @test sum(abs2, sa) === sum(abs2, a)
         @test sum(sa, dims=2) === RSArray2(sum(a, dims=2))
+        @test sum(sa, dims=(2,)) === RSArray2(sum(a, dims=2))
         @test sum(sa, dims=Val(2)) === RSArray2(sum(a, dims=2))
+        @test sum(sa, dims=(1,3)) === RSArray13(sum(a, dims=(1,3)))
         @test sum(abs2, sa; dims=2) === RSArray2(sum(abs2, a, dims=2))
+        @test sum(abs2, sa; dims=(2,)) === RSArray2(sum(abs2, a, dims=2))
         @test sum(abs2, sa; dims=Val(2)) === RSArray2(sum(abs2, a, dims=2))
 
         @test prod(sa) === prod(a)