The following pictures show L's (with short side 1) packed inside the smallest known tan (with short side s).

1.

2.

3.

s = 3

Trivial.
s = 3√2 = 4.242+

Trivial.
s = 5

Trivial.

4.

5.

6.-7.

s = 4√2 = 5.656+

Found by Maurizio Morandi

in July 2012
s = 2 + 3√2 = 6.242+

Found by Maurizio Morandi

in July 2012.
s = 7

Trivial.

8.

9.

10.

s = 11/√2 = 7.778+

Trivial.
s = 8

Trivial.
s = 6√2 = 8.485+

Trivial.

11.-12.

13.

14.

s = 9

Trivial.

s = 2 + 11/√2 = 9.778+

Found by Maurizio Morandi

in July 2012.
s = 7√2 = 9.899+

Trivial.

15.

16.

17.-18.

s = 10

Trivial.
s = 15/√2 = 10.606+

Trivial.
s = 11

Trivial.