diff --git a/Project.toml b/Project.toml
index 9dbb81c..85c389e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,7 +3,7 @@ uuid = "6f1fad26-d15e-5dc8-ae53-837a1d7b8c9f"
 license = "MIT"
 desc = "Tape based task copying in Turing"
 repo = "https://github.com/TuringLang/Libtask.jl.git"
-version = "0.8"
+version = "0.8.1"
 
 [deps]
 FunctionWrappers = "069b7b12-0de2-55c6-9aab-29f3d0a68a2e"
diff --git a/src/tapedfunction.jl b/src/tapedfunction.jl
index 88a7b90..1f78c42 100644
--- a/src/tapedfunction.jl
+++ b/src/tapedfunction.jl
@@ -58,9 +58,9 @@ mutable struct TapedFunction{F, TapeType}
     binding_values::Bindings
     arg_binding_slots::Vector{Int} # arg indices in binding_values
     retval_binding_slot::Int # 0 indicates the function has not returned
-    deepcopy_types::Vector{Any}
+    deepcopy_types::Type # use a Union type for multiple types
 
-    function TapedFunction{F, T}(f::F, args...; cache=false, deepcopy_types=[]) where {F, T}
+    function TapedFunction{F, T}(f::F, args...; cache=false, deepcopy_types=Union{}) where {F, T}
         args_type = _accurate_typeof.(args)
         cache_key = (f, args_type...)
 
@@ -78,7 +78,7 @@ mutable struct TapedFunction{F, TapeType}
         return tf
     end
 
-    TapedFunction(f, args...; cache=false, deepcopy_types=[]) =
+    TapedFunction(f, args...; cache=false, deepcopy_types=Union{}) =
         TapedFunction{typeof(f), RawTape}(f, args...; cache=cache, deepcopy_types=deepcopy_types)
 
     function TapedFunction{F, T0}(tf::TapedFunction{F, T1}) where {F, T0, T1}
@@ -472,7 +472,7 @@ tape_shallowcopy(x::Core.Box) = Core.Box(tape_shallowcopy(x.contents))
 tape_deepcopy(x::Core.Box) = Core.Box(tape_deepcopy(x.contents))
 
 function _tape_copy(v, deepcopy_types)
-    if any(t -> isa(v, t), deepcopy_types)
+    if isa(v, deepcopy_types)
         tape_deepcopy(v)
     else
         tape_shallowcopy(v)
diff --git a/src/tapedtask.jl b/src/tapedtask.jl
index 150cdfe..c5e5d22 100644
--- a/src/tapedtask.jl
+++ b/src/tapedtask.jl
@@ -65,12 +65,13 @@ end
 
 # NOTE: evaluating model without a trace, see
 # https://github.com/TuringLang/Turing.jl/pull/1757#diff-8d16dd13c316055e55f300cd24294bb2f73f46cbcb5a481f8936ff56939da7ceR329
-function TapedTask(f, args...; deepcopy_types=[Array, Ref]) # deepcoy Array and Ref by default.
+function TapedTask(f, args...; deepcopy_types=Union{Array, Ref}) # deepcoy Array and Ref by default.
     tf = TapedFunction(f, args...; cache=true, deepcopy_types=deepcopy_types)
     TapedTask(tf, args...)
 end
 
-TapedTask(t::TapedTask, args...) = TapedTask(func(t), args...)
+TapedTask(finfo::Tuple{Any, Type}, args...) = TapedTask(finfo[1], args...; deepcopy_types=finfo[2])
+TapedTask(t::TapedTask, args...) = TapedTask(func(t), args...; deepcopy_types=t.tf.deepcopy_types)
 func(t::TapedTask) = t.tf.func
 
 #=
diff --git a/test/tapedtask.jl b/test/tapedtask.jl
index e49d5bb..f55f83e 100644
--- a/test/tapedtask.jl
+++ b/test/tapedtask.jl
@@ -1,4 +1,20 @@
 @testset "tapedtask" begin
+    @testset "construction" begin
+        function f()
+            t = 1
+            while true
+                produce(t)
+                t = 1 + t
+            end
+        end
+
+        ttask = TapedTask(f)
+        @test consume(ttask) == 1
+
+        ttask = TapedTask((f, Union{}))
+        @test consume(ttask) == 1
+    end
+
     @testset "iteration" begin
         function f()
             t = 1