Planing thin lumber

[kenmaven]

I'm building a scroll saw cathedral and the plan calls for some pieces 1/16" thick.
I resaw my hardwood for the various thicknesses I need but my planer doesn't plane less than 1/8".
I thought of mounting the piece I want to plane onto another board with double sided tape but I know the thinly planed wood would break when I try to free it from the tape.
Any suggestions?

[UHMNL]

I have a 2x10 board on the bottom. Have a nail on the end, so it will not slide.
Have planed many pieces of 1/16"
Mike

[pierre62]

For me i screw a vice on piece of plywood.

[BilltheDiver]

Maybe find a friend with a wide drum sander?

[EIEIO]

Do you need it planed on both sides? How about resaw slicing 1/16" off a dressed 3/4" board, then plane the surface of the remaining thick part of the board and resaw another 1/16" etc. Then you wind up with 1/16" boards that are planed on one side (outside surface) but rough on other (inside of cathedral).

[xuryl]

I use a plywood insert with a 2 x 3 stop, to plane down to 1/16". It needs to be long enough to cover both the infeed and outfeed tables. I finished it with polyurethane and a good coat of paste wax.

[kenmaven]

Thanks Guys'
All good solutions!
I ended up buying a 4'x 12" melamine shelf board and glued stops on the underside.  It extends about six inches on each side of the in/out feed table.  The stops should keep it from sliding.
Like many such problems, the solution is so simple---why didn't I think of that?
Thanks for your suggestions.