diff --git a/base/array.jl b/base/array.jl
index 7676b380923ee..fb702725b389a 100644
--- a/base/array.jl
+++ b/base/array.jl
@@ -529,6 +529,7 @@ function fill end
 fill(v, dims::DimOrInd...) = fill(v, dims)
 fill(v, dims::NTuple{N, Union{Integer, OneTo}}) where {N} = fill(v, map(to_dim, dims))
 fill(v, dims::NTuple{N, Integer}) where {N} = (a=Array{typeof(v),N}(undef, dims); fill!(a, v); a)
+fill(v, dims::NTuple{N, DimOrInd}) where {N} = (a=similar(Array{typeof(v),N}, dims); fill!(a, v); a)
 fill(v, dims::Tuple{}) = (a=Array{typeof(v),0}(undef, dims); fill!(a, v); a)
 
 """
@@ -589,6 +590,11 @@ for (fname, felt) in ((:zeros, :zero), (:ones, :one))
             fill!(a, $felt(T))
             return a
         end
+        function $fname(::Type{T}, dims::NTuple{N, DimOrInd}) where {T,N}
+            a = similar(Array{T,N}, dims)
+            fill!(a, $felt(T))
+            return a
+        end
     end
 end
 
diff --git a/base/bitarray.jl b/base/bitarray.jl
index 079dbefe03a94..f7eeafbb62231 100644
--- a/base/bitarray.jl
+++ b/base/bitarray.jl
@@ -404,6 +404,7 @@ falses(dims::DimOrInd...) = falses(dims)
 falses(dims::NTuple{N, Union{Integer, OneTo}}) where {N} = falses(map(to_dim, dims))
 falses(dims::NTuple{N, Integer}) where {N} = fill!(BitArray(undef, dims), false)
 falses(dims::Tuple{}) = fill!(BitArray(undef, dims), false)
+falses(dims::NTuple{N, DimOrInd}) where {N} = fill!(similar(BitArray, dims), false)
 
 """
     trues(dims)
@@ -422,6 +423,7 @@ trues(dims::DimOrInd...) = trues(dims)
 trues(dims::NTuple{N, Union{Integer, OneTo}}) where {N} = trues(map(to_dim, dims))
 trues(dims::NTuple{N, Integer}) where {N} = fill!(BitArray(undef, dims), true)
 trues(dims::Tuple{}) = fill!(BitArray(undef, dims), true)
+trues(dims::NTuple{N, DimOrInd}) where {N} = fill!(similar(BitArray, dims), true)
 
 function one(x::BitMatrix)
     m, n = size(x)
diff --git a/test/abstractarray.jl b/test/abstractarray.jl
index a0a6ba6b2229a..feb6adaf39fdd 100644
--- a/test/abstractarray.jl
+++ b/test/abstractarray.jl
@@ -11,6 +11,9 @@ using .Main.StructArrays
 isdefined(Main, :FillArrays) || @eval Main include("testhelpers/FillArrays.jl")
 using .Main.FillArrays
 
+isdefined(Main, :SizedArrays) || @eval Main include("testhelpers/SizedArrays.jl")
+using .Main.SizedArrays
+
 A = rand(5,4,3)
 @testset "Bounds checking" begin
     @test checkbounds(Bool, A, 1, 1, 1) == true
@@ -2097,3 +2100,22 @@ end
         @test r2[i] == z[j]
     end
 end
+
+@testset "zero for arbitrary axes" begin
+    r = SizedArrays.SOneTo(2)
+    s = Base.OneTo(2)
+    _to_oneto(x::Integer) = Base.OneTo(2)
+    _to_oneto(x::Union{Base.OneTo, SizedArrays.SOneTo}) = x
+    for (f, v) in ((zeros, 0), (ones, 1), ((x...)->fill(3,x...),3))
+        for ax in ((r,r), (s, r), (2, r))
+            A = f(ax...)
+            @test axes(A) == map(_to_oneto, ax)
+            if all(x -> x isa SizedArrays.SOneTo, ax)
+                @test A isa SizedArrays.SizedArray && parent(A) isa Array
+            else
+                @test A isa Array
+            end
+            @test all(==(v), A)
+        end
+    end
+end
diff --git a/test/bitarray.jl b/test/bitarray.jl
index 056a201bd4f6f..2cf285370441e 100644
--- a/test/bitarray.jl
+++ b/test/bitarray.jl
@@ -3,6 +3,9 @@
 using Base: findprevnot, findnextnot
 using Random, LinearAlgebra, Test
 
+isdefined(Main, :SizedArrays) || @eval Main include("testhelpers/SizedArrays.jl")
+using .Main.SizedArrays
+
 tc(r1::NTuple{N,Any}, r2::NTuple{N,Any}) where {N} = all(x->tc(x...), [zip(r1,r2)...])
 tc(r1::BitArray{N}, r2::Union{BitArray{N},Array{Bool,N}}) where {N} = true
 tc(r1::SubArray{Bool,N1,BitArray{N2}}, r2::SubArray{Bool,N1,<:Union{BitArray{N2},Array{Bool,N2}}}) where {N1,N2} = true
@@ -82,6 +85,25 @@ allsizes = [((), BitArray{0}), ((v1,), BitVector),
     @test !isassigned(b, length(b) + 1)
 end
 
+@testset "trues and falses with custom axes" begin
+    for ax in ((SizedArrays.SOneTo(2),), (SizedArrays.SOneTo(2), Base.OneTo(2)))
+        t = trues(ax)
+        if all(x -> x isa SizedArrays.SOneTo, ax)
+            @test t isa SizedArrays.SizedArray && parent(t) isa BitArray
+        else
+            @test t isa BitArray
+        end
+        @test all(t)
+
+        f = falses(ax)
+        if all(x -> x isa SizedArrays.SOneTo, ax)
+            @test t isa SizedArrays.SizedArray && parent(t) isa BitArray
+        else
+            @test t isa BitArray
+        end
+        @test !any(f)
+    end
+end
 
 @testset "Conversions for size $sz" for (sz, T) in allsizes
     b1 = rand!(falses(sz...))
diff --git a/test/testhelpers/SizedArrays.jl b/test/testhelpers/SizedArrays.jl
index 43bc27e630479..2d37cead61a08 100644
--- a/test/testhelpers/SizedArrays.jl
+++ b/test/testhelpers/SizedArrays.jl
@@ -43,10 +43,25 @@ Base.size(a::SizedArray) = size(typeof(a))
 Base.size(::Type{<:SizedArray{SZ}}) where {SZ} = SZ
 Base.axes(a::SizedArray) = map(SOneTo, size(a))
 Base.getindex(A::SizedArray, i...) = getindex(A.data, i...)
+Base.setindex!(A::SizedArray, v, i...) = setindex!(A.data, v, i...)
 Base.zero(::Type{T}) where T <: SizedArray = SizedArray{size(T)}(zeros(eltype(T), size(T)))
+Base.parent(S::SizedArray) = S.data
 +(S1::SizedArray{SZ}, S2::SizedArray{SZ}) where {SZ} = SizedArray{SZ}(S1.data + S2.data)
 ==(S1::SizedArray{SZ}, S2::SizedArray{SZ}) where {SZ} = S1.data == S2.data
 
+homogenize_shape(t::Tuple) = (_homogenize_shape(first(t)), homogenize_shape(Base.tail(t))...)
+homogenize_shape(::Tuple{}) = ()
+_homogenize_shape(x::Integer) = x
+_homogenize_shape(x::AbstractUnitRange) = length(x)
+const Dims = Union{Integer, Base.OneTo, SOneTo}
+function Base.similar(::Type{A}, shape::Tuple{Dims, Vararg{Dims}}) where {A<:AbstractArray}
+    similar(A, homogenize_shape(shape))
+end
+function Base.similar(::Type{A}, shape::Tuple{SOneTo, Vararg{SOneTo}}) where {A<:AbstractArray}
+    R = similar(A, length.(shape))
+    SizedArray{length.(shape)}(R)
+end
+
 const SizedMatrixLike = Union{SizedMatrix, Transpose{<:Any, <:SizedMatrix}, Adjoint{<:Any, <:SizedMatrix}}
 
 _data(S::SizedArray) = S.data