Thicknessing thin wood strip below 5 mm is a bit like planing any thicker board but requires a fixture and extra care as regard the workpiece. Here is my way of planing down to about 2mm thick (1/12") with an auxiliary table raising the planer bed that purposes wood stocks over 400 mm in length. The thin sheet of wood freely glides on the waxed sled top without lead or trail edge stop which means no glue or double stick tape to hold the strip.

You may see in the below drawing what should be the grain direction and the arch orientation for the workpiece to go through the working tool. Whatever the increment depth of each pass, they are main issues that also lead to exclude counter grain in a single piece, highly figured or stress cracked or checked wood, weak density and so forth.

The fixture merely recreates the planer bed with two side guides protruding about 1.5mm (1/16") and preventing the workpiece from going out the bed. Although not required, the stop block screwed under the back side aims safety purposes.

The first time I fed the workpiece through the planer made me confused. The wood bed lifted the anti-kickback pawls and I expected the fixture to slide with the wood strip.

But as soon as the v-grooved infeed roller caught the wood, only the workpiece kept going and I had to slightly push the auxiliary bed so that both reached together the smooth outfeed roller.

At that stage the fixture correctly held the workpiece. I released the work and went at the rear machine to retrieve the planed strip. Mind the underneath stop that didn't contact the edge of the cast iron bed. Actually I dont remember it has ever done.