diff --git a/src/Tracing.jl b/src/Tracing.jl
index 76710c58d..6e16e424d 100644
--- a/src/Tracing.jl
+++ b/src/Tracing.jl
@@ -867,7 +867,14 @@ end
 
 append_path(path, i) = (path..., i)
 
-function make_tracer(seen, prev::RT, path, mode; toscalar=false, tobatch=nothing) where {RT}
+function make_tracer(
+    seen,
+    @nospecialize(prev::RT),
+    @nospecialize(path),
+    mode;
+    toscalar=false,
+    tobatch=nothing,
+) where {RT}
     if haskey(seen, prev)
         return seen[prev]
     end
@@ -944,7 +951,9 @@ function make_tracer(seen, prev::RT, path, mode; toscalar=false, tobatch=nothing
     return y
 end
 
-function make_tracer(seen, prev::ConcreteRArray{T,N}, path, mode; kwargs...) where {T,N}
+function make_tracer(
+    seen, @nospecialize(prev::ConcreteRArray{T,N}), @nospecialize(path), mode; kwargs...
+) where {T,N}
     if mode == ArrayToConcrete
         return prev
     end
@@ -961,7 +970,12 @@ function make_tracer(seen, prev::ConcreteRArray{T,N}, path, mode; kwargs...) whe
 end
 
 function make_tracer(
-    seen, prev::TracedRArray{T,N}, path, mode; toscalar=false, tobatch=nothing
+    seen,
+    @nospecialize(prev::TracedRArray{T,N}),
+    @nospecialize(path),
+    mode;
+    toscalar=false,
+    tobatch=nothing,
 ) where {T,N}
     if mode == ConcreteToTraced
         throw("Cannot trace existing trace type")
@@ -1000,12 +1014,21 @@ function make_tracer(
     throw("Cannot Unknown trace mode $mode")
 end
 
-make_tracer(seen, prev::RT, path, mode; kwargs...) where {RT<:AbstractFloat} = prev
+function make_tracer(
+    seen, @nospecialize(prev::RT), @nospecialize(path), mode; kwargs...
+) where {RT<:AbstractFloat}
+    return prev
+end
 
-make_tracer(seen, prev::Symbol, path, mode; kwargs...) = prev
+make_tracer(seen, prev::Symbol, @nospecialize(path), mode; kwargs...) = prev
 
 function make_tracer(
-    seen, prev::Complex{RT}, path, mode; toscalar=false, tobatch=nothing
+    seen,
+    @nospecialize(prev::Complex{RT}),
+    @nospecialize(path),
+    mode;
+    toscalar=false,
+    tobatch=nothing,
 ) where {RT}
     return Complex(
         make_tracer(seen, prev.re, append_path(path, :re), mode; toscalar, tobatch),
@@ -1013,7 +1036,9 @@ function make_tracer(
     )
 end
 
-function make_tracer(seen, prev::RT, path, mode; kwargs...) where {RT<:Array}
+function make_tracer(
+    seen, @nospecialize(prev::RT), @nospecialize(path), mode; kwargs...
+) where {RT<:Array}
     if haskey(seen, prev)
         return seen[prev]
     end
@@ -1041,7 +1066,9 @@ function make_tracer(seen, prev::RT, path, mode; kwargs...) where {RT<:Array}
     return newa
 end
 
-function make_tracer(seen, prev::RT, path, mode; kwargs...) where {RT<:Tuple}
+function make_tracer(
+    seen, @nospecialize(prev::RT), @nospecialize(path), mode; kwargs...
+) where {RT<:Tuple}
     return (
         (
             make_tracer(seen, v, append_path(path, i), mode; kwargs...) for
@@ -1050,7 +1077,9 @@ function make_tracer(seen, prev::RT, path, mode; kwargs...) where {RT<:Tuple}
     )
 end
 
-function make_tracer(seen, prev::NamedTuple{A,RT}, path, mode; kwargs...) where {A,RT}
+function make_tracer(
+    seen, @nospecialize(prev::NamedTuple{A,RT}), @nospecialize(path), mode; kwargs...
+) where {A,RT}
     return NamedTuple{A,traced_type(RT, (), Val(mode))}((
         (
             make_tracer(
@@ -1060,7 +1089,7 @@ function make_tracer(seen, prev::NamedTuple{A,RT}, path, mode; kwargs...) where
     ))
 end
 
-function make_tracer(seen, prev::Core.Box, path, mode; kwargs...)
+function make_tracer(seen, prev::Core.Box, @nospecialize(path), mode; kwargs...)
     if haskey(seen, prev)
         return seen[prev]
     end