diff --git a/src/Bijectors.jl b/src/Bijectors.jl
index e435ebf7..6991d446 100644
--- a/src/Bijectors.jl
+++ b/src/Bijectors.jl
@@ -243,8 +243,6 @@ end
 
 include("interface.jl")
 
-# Broadcasting here breaks Tracker for some reason
-maporbroadcast(f, x::AbstractArray{<:Any, N}...) where {N} = map(f, x...)
 maporbroadcast(f, x::AbstractArray...) = f.(x...)
 
 # optional dependencies
diff --git a/src/compat/tracker.jl b/src/compat/tracker.jl
index cb8d6549..f0dea430 100644
--- a/src/compat/tracker.jl
+++ b/src/compat/tracker.jl
@@ -12,14 +12,18 @@ using .Tracker: Tracker,
 using Compat: eachcol
 using LinearAlgebra
 
+# Broadcasting here breaks Tracker
+const TrackedT = Union{TrackedArray, AbstractArray{<:TrackedReal}}
 maporbroadcast(f, x::TrackedArray...) = f.(x...)
-function maporbroadcast(
-    f,
-    x1::TrackedArray{T, N},
-    x::AbstractArray{<:TrackedReal}...,
-) where {T, N}
-    return f.(convert(Array{TrackedReal{T}, N}, x1), x...)
-end
+maporbroadcast(f, x::Union{TrackedArray, AbstractArray{<:TrackedReal}}...) = map(f, x...)
+maporbroadcast(f, x1::TrackedT, x2::AbstractArray) = map(f, x1, x2)
+maporbroadcast(f, x1::AbstractArray, x2::TrackedT) = map(f, x1, x2)
+maporbroadcast(f, x1::TrackedT, x2::AbstractArray, x3::AbstractArray) = map(f, x1, x2, x3)
+maporbroadcast(f, x1::AbstractArray, x2::TrackedT, x3::AbstractArray) = map(f, x1, x2, x3)
+maporbroadcast(f, x1::AbstractArray, x2::AbstractArray, x3::TrackedT) = map(f, x1, x2, x3)
+maporbroadcast(f, x1::TrackedT, x2::TrackedT, x3::AbstractArray) = map(f, x1, x2, x3)
+maporbroadcast(f, x1::AbstractArray, x2::TrackedT, x3::TrackedT) = map(f, x1, x2, x3)
+maporbroadcast(f, x1::TrackedT, x2::AbstractArray, x3::TrackedT) = map(f, x1, x2, x3)
 
 _eps(::Type{<:TrackedReal{T}}) where {T} = _eps(T)
 function Base.minimum(d::LocationScale{<:TrackedReal})
diff --git a/test/runtests.jl b/test/runtests.jl
index 47f36d95..3e4a364a 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -35,5 +35,11 @@ end
 
 if !is_TRAVIS && (GROUP == "All" || GROUP == "AD")
     include("ad/distributions.jl")
+    if AD == "All" || AD == "ReverseDiff" 
+        @testset "Turing issue 1385" begin
+            dist = arraydist(truncated.(Laplace.(0, [1, 2]), -10.0, 70.0))
+            x = ReverseDiff.track(rand(dist))
+            @test typeof(bijector(dist)(x)) <: ReverseDiff.TrackedArray
+        end
+    end
 end
-