What about Isla ? I really like this one ;-)
Ida is very sweet and retro! I do love the short and sweet names. If you're looking for a sliightly more modern name I would suggest Ada, which is a personal favourite
Other short and sweet names:
Anya
Calla
Cleo
Esme
Eve
Faye
Io
Ivy
Kira
Lea
Lena
Lida
Lila
Luna
Maia
Mara
Maya
Mia
Nina
Phoebe
Vera
Zoe