In previous thread an efficient way to remove empty lists ({}) from lists was suggested:

Replace[expr, x_List :> DeleteCases[x, {}], {0, Infinity}]

Using the Trott-Strzebonski in-place evaluation technique this method can be generalized for working also with held expressions:

f1[expr_] := 
 Replace[expr, 
  x_List :> With[{eval = DeleteCases[x, {}]}, eval /; True], {0, Infinity}]

This solution is more efficient than the one based on ReplaceRepeated:

f2[expr_] := expr //. {left___, {}, right___} :> {left, right}

But it has one disadvantage: it evaluates held expressions if they are wrapped by List:

In[20]:= f1[Hold[{{}, 1 + 1}]]

Out[20]= Hold[{2}]

So my question is: what is the most efficient way to remove all empty lists ({}) from lists without evaluating held expressions? The empty List[] object should be removed only if it is an element of another List itself.

Here are some timings:

In[76]:= expr = Tuples[Tuples[{{}, {}}, 3], 4];
First@Timing[#[expr]] & /@ {f1, f2, f3}
pl = Plot3D[Sin[x y], {x, 0, Pi}, {y, 0, Pi}]; 
First@Timing[#[pl]] & /@ {f1, f2, f3}

Out[77]= {0.581, 0.901, 5.027}

Out[78]= {0.12, 0.21, 0.18}

Definitions:

Clear[f1, f2, f3];
f3[expr_] := 
  FixedPoint[
   Function[e, Replace[e, {a___, {}, b___} :> {a, b}, {0, Infinity}]], expr];
f1[expr_] := 
  Replace[expr, 
   x_List :> With[{eval = DeleteCases[x, {}]}, eval /; True], {0, Infinity}];
f2[expr_] := expr //. {left___, {}, right___} :> {left, right};