Removing row with smallest value, for a given factor

I have a table.
First column is a date, second column is an index and other columns contains some other values.
I want to remove, for each date, the row with the smallest index (it is not necessarily 1).

ex: in the following table, I want to remove row 1 (2013-05-12 with index 2) and row 8 (2013-05-13 with index 1)

? ? ? ? ? ?day index values
1 ? ?2013-05-12 ? ?2 ?xxxx
2 ? ?2013-05-12 ? ?3 ?xxxx
3 ? ?2013-05-12 ? ?4 ?xxxx
4 ? ?2013-05-12 ? ?5 ?xxxx
5 ? ?2013-05-12 ? ?6 ?xxxx
6 ? ?2013-05-12 ? ?7 ?xxxx
7 ? ?2013-05-12 ? ?8 ?xxxx
8 ? ?2013-05-13 ? ?1 ?xxxx
9 ? ?2013-05-13 ? ?3 ?xxxx
10 ? 2013-05-13 ? ?4 ?xxxx
11 ? 2013-05-13 ? ?5 ?xxxx
12 ? 2013-05-13 ? ?6 ?xxxx
13 ? 2013-05-13 ? ?7 ?xxxx
14 ? 2013-05-13 ? ?8 ?xxxx
15 ? 2013-05-13 ? ?9 ?xxxx
16 ? 2013-05-13 ? 10 ?xxxx
17 ? 2013-05-13 ? 12 ?xxxx


Thank you for your help