diff --git a/src/OffsetArrays.jl b/src/OffsetArrays.jl
index b4dfde2..0851588 100644
--- a/src/OffsetArrays.jl
+++ b/src/OffsetArrays.jl
@@ -319,15 +319,23 @@ Base.similar(A::OffsetArray, ::Type{T}, dims::Dims) where T =
     similar(parent(A), T, dims)
 
 """
-    isonebased(ax::AbstractUnitRange{<:Integer})
+    isonebased(::Type{T}) where {T<:AbstractUnitRange{<:Integer}}
 
-Return whether `firstindex(ax)` is statically known to be `1`. Custom axis types may extend this method
-to ensure that the axis offset is ignored, for example in `similar`.
+Return whether `first(ax::T)` is statically known to be `1` for any `ax` of type `T`
+(`false` by default).
+Custom axis types may extend this method to ensure that the axis offset is ignored,
+for example in `similar`. This may strip `OffsetArray` wrappers on occasion, or dispatch
+to `Base` methods for 1-based axes.
+
+For axes that are essentially wrappers around another `AbstractUnitRange`,
+and share their indexing with their parents, one may forward the type of the
+parent range to `isonebased`.
 """
-isonebased(_) = false
-isonebased(::Integer) = true
-isonebased(::Base.OneTo) = true
-isonebased(r::IIUR) = isonebased(r.indices)
+isonebased(x) = isonebased(typeof(x))
+isonebased(::Type) = false
+isonebased(::Type{<:Integer}) = true
+isonebased(::Type{<:Base.OneTo}) = true
+isonebased(::Type{IdentityUnitRange{T}}) where {T} = isonebased(T)
 
 # Since the following is committing type-piracy, we provide an opt-out mechanism to the users
 function Base.similar(A::AbstractArray, ::Type{T}, shape::Tuple{OffsetAxisKnownLength,Vararg{OffsetAxisKnownLength}}) where T
diff --git a/test/runtests.jl b/test/runtests.jl
index 300a18d..4b54cd3 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -9,7 +9,7 @@ using EllipsisNotation
 using FillArrays
 using LinearAlgebra
 using OffsetArrays
-using OffsetArrays: IdentityUnitRange, no_offset_view, IIUR, Origin, IdOffsetRange
+using OffsetArrays: IdentityUnitRange, no_offset_view, IIUR, Origin, IdOffsetRange, isonebased
 using StaticArrays
 using Test
 
@@ -2262,6 +2262,14 @@ Base.size(x::PointlessWrapper) = size(parent(x))
 Base.axes(x::PointlessWrapper) = axes(parent(x))
 Base.getindex(x::PointlessWrapper, i...) = x.parent[i...]
 
+@testset "isonebased" begin
+    @test isonebased(Base.OneTo(2))
+    @test !isonebased(1:2)
+    @test isonebased(IdentityUnitRange(Base.OneTo(2)))
+    @test !isonebased(IdentityUnitRange(1:2))
+    @test similar(zeros(1), Int, IdentityUnitRange(Base.OneTo(2))) isa Vector{Int}
+end
+
 @testset "no offset view" begin
     # OffsetArray fallback
     A = randn(3, 3)