diff --git a/src/data/writing_datatypes.jl b/src/data/writing_datatypes.jl
index 68570202..91c9f9f4 100644
--- a/src/data/writing_datatypes.jl
+++ b/src/data/writing_datatypes.jl
@@ -446,6 +446,11 @@ end
 
 function h5convert!(out::Pointers, ::DataTypeODR, f::JLDFile, T::DataType, wsession::JLDWriteSession)
     t = typename(T)
+    if T <: Function && isgensym(nameof(T.instance))
+        @warn LazyString("Attempting to store ", T, ".\n",
+                         "JLD2 only stores functions by name.\n",
+                         " This may not be useful for anonymous functions.")
+    end
     store_vlen!(out, UInt8, f, unsafe_wrap(Vector{UInt8}, t), f.datatype_wsession)
     if isempty(T.parameters)
         h5convert_uninitialized!(out+odr_sizeof(Vlen{UInt8}), Vlen{UInt8})
@@ -627,9 +632,6 @@ end
 # fieldodr, but actually encoding the data for things that odr stores
 # as references
 @nospecializeinfer function odr(@nospecialize(T::Type))
-    if T <: Function
-        @warn LazyString("Attempting to store ", T, ".\n Function types cannot be propertly stored in JLD2 files.\n Loading may yield unexpected results.")
-    end
     if !hasdata(T)
         # A pointer singleton or ghost. We need to write something, but we'll
         # just write a single byte.
diff --git a/src/julia_compat.jl b/src/julia_compat.jl
index f17e348e..a577bebb 100644
--- a/src/julia_compat.jl
+++ b/src/julia_compat.jl
@@ -28,4 +28,10 @@ end
     end
 else
     using Base: @nospecializeinfer
+end
+
+@static if VERSION < v"1.7.0"
+    isgensym(s::Symbol) = '#' in string(s)
+else
+    using Base: isgensym
 end
\ No newline at end of file
diff --git a/test/loadsave.jl b/test/loadsave.jl
index ec87d90b..943ebc3c 100644
--- a/test/loadsave.jl
+++ b/test/loadsave.jl
@@ -764,14 +764,7 @@ end
         eval(:(module ModuleWithFunction
             fun(x) = x+1
         end))
-        if VERSION ≥ v"1.7"
-            @test_warn(
-                contains("Function types cannot"),
-                eval(:(save_object("test.jld2", (1, ModuleWithFunction.fun, 2))))
-            )
-        else
-            eval(:(save_object("test.jld2", (1, ModuleWithFunction.fun, 2))))
-        end
+        eval(:(save_object("test.jld2", (1, ModuleWithFunction.fun, 2))))
         obj = load_object("test.jld2")
         @test length(obj) == 3
         @test obj[1] == 1