Ron Guth: The first modification to the Liberty Seated dime design took place in 1838, when 13 stars were added to the obverse in a large arc around Miss Liberty following an order from Mint Director Robert Maskell Patterson. Until 1840, the "With Stars" dimes were created using a hub of the No Stars design, followed by the addition of the stars by hand. The 1838 Small Stars resulted from the use of star punches for half dimes. Die clashing created the "Partial Drapery" variety of 1838, where the reversed impression of the E of DIME can be seen beneath Liberty's arm (holding the pole).
Sources and/or recommended reading:
"Walter Breen's Complete Encyclopedia of U.S. and Colonial Coins" by Walter Breen