There is a very special property common to all the words below:
ART
BAIL
LAP
LATTE
MEAT
ON
PEAR
PEAS
RED
RUM
SCENE
SHOT
SIGN
TINES
Stuck? Need a hint? Here's that list again:
ART
BAIL
LAP
LATTE
MEAT
ON
PEAR
PEAS
RED
RUM
SCENE
SHOT
SIGN
TINES
Epilogue:
Fast solve, @Deusovi !
One minor variant:
Another anagram for LAP+LAP is APPALL