diff --git a/src/decomposition.jl b/src/decomposition.jl
index 973cf04..b0e00e3 100644
--- a/src/decomposition.jl
+++ b/src/decomposition.jl
@@ -11,7 +11,7 @@ function register_decomposition(model::JuMP.Model)
     # Link to the tree
     tree = gettree(model)
     tree === nothing && return
-    for (key, jump_obj) in model.obj_dict
+    for (_, jump_obj) in model.obj_dict
         _annotate_elements!(model, jump_obj, tree)
     end
     return
@@ -122,7 +122,7 @@ function MOI.get(
     tree === nothing && return nothing
 
     conattr = get(dest.conattr, attribute, nothing)
-    conattr === nothing && return tree.root.master
+    conattr === nothing && return nothing # anonymous constraint
     return get(conattr, ci, tree.root.master)
 end
 
@@ -134,7 +134,7 @@ function MOI.get(
     tree === nothing && return nothing
 
     varattr = get(dest.varattr, attribute, nothing)
-    varattr === nothing && return tree.root.master
+    varattr === nothing && return nothing # anonymous variable
     return get(varattr, vi, tree.root.master)
 end
 
diff --git a/test/dantzigwolfe.jl b/test/dantzigwolfe.jl
index 727df9e..a9df99a 100644
--- a/test/dantzigwolfe.jl
+++ b/test/dantzigwolfe.jl
@@ -161,8 +161,8 @@ function dummymodel3()
     model = BD.BlockModel()
     BD.@axis(A, 1:5)
     B = 1:6
-    @variable(model, x[a in A, b in B], Int)
-    mast = @constraint(model, sum(x[a,b] for a in A, b in B) >= 5)
+    x = @variable(model, [a in A, b in B], Int) # anonymous variables
+    mast = @constraint(model, sum(x[a,b] for a in A, b in B) >= 5) # anonymous constraints
     sp = @constraint(model, [a in A], sum(x[a,b] for b in B) == 1) # anonymous constraints
     @objective(model, Min, sum(x[a,b] for a in A, b in B))
     @dantzig_wolfe_decomposition(model, dec, A)
@@ -209,17 +209,19 @@ function test_dummy_model_decompositions()
         @test MOI.get(model, BD.ObjectiveDualBound()) === nothing
     end
 
-    @testset "Model with anonymous constraint" begin
+    @testset "Model with anonymous variables & constraints" begin
         model, x, mast, sp, dec = dummymodel3()
         try
             JuMP.optimize!(model)
         catch e
             @test e isa NoOptimizer
         end
+        x_annotation = BD.annotation(model, x[1,1])
+        @test x_annotation === nothing
         mast_annotation = BD.annotation(model, mast)
-        test_annotation(mast_annotation, BD.Master, BD.DantzigWolfe, 1, 1)
+        @test mast_annotation === nothing # anonymous constraint
         sp_annotation = BD.annotation(model, sp[1])
-        test_annotation(sp_annotation, BD.Master, BD.DantzigWolfe, 1, 1)
+        @test sp_annotation === nothing # anonymous constraint
     end
     return
 end