diff --git a/src/generator.jl b/src/generator.jl
index be47e62..8619deb 100644
--- a/src/generator.jl
+++ b/src/generator.jl
@@ -47,6 +47,31 @@ function Base.collect(itr::DiskGenerator{<:AbstractArray{<:Any,N}}) where {N}
     return dest
 end
 
+# Warning: this is not public API!
+function Base.collect_similar(A::AbstractArray, itr::DiskGenerator{<:AbstractArray{<:Any,N}}) where {N}
+    y = iterate(itr)
+    shp = axes(itr.iter)
+    if y === nothing
+        et = Base.@default_eltype(itr)
+        return similar(A, et, shp)
+    end
+    v1, st = y
+    dest = similar(A, typeof(v1), shp)
+    i = y
+    for I in eachindex(itr.iter)
+        if i isa Nothing # Mainly to keep JET clean 
+            error(
+                "Should not be reached: iterator is shorter than its `eachindex` iterator"
+            )
+        else
+            dest[I] = first(i)
+            i = iterate(itr, last(i))
+        end
+    end
+    return dest
+
+end
+
 macro implement_generator(t)
     t = esc(t)
     quote
diff --git a/test/runtests.jl b/test/runtests.jl
index db8dd1c..5c9a487 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -953,3 +953,17 @@ end
     @test getindex_count(A) == 0 
 end
 
+@testset "Map over indices correctly" begin
+    # This is a regression test for issue #144
+    # `map` should always work over the correct indices,
+    # especially since we overload generators to `DiskArrayGenerator`.
+
+    data = [i+j for i in 1:200, j in 1:100]
+    da = AccessCountDiskArray(data, chunksize=(10,10))
+    @test map(identity, da) == data
+    @test all(map(identity, da) .== data)
+
+    # Make sure that type inference works
+    @inferred Matrix{Int} map(identity, da)
+    @inferred Matrix{Float64} map(x -> x * 5.0, da)
+end