Jessica Biel became ''obsessed'' with trying to keep her recent wedding a secret.

The 'Hitchcock' actress - who married 'Cry Me A River' singer Justin Timberlake in front of more than 100 close friends and family at the plush Borgo Egnazia resort in Puglia, Southern Italy, on October 19 - compared their wedding plans to a covert CIA operation but admitted they still couldn't prevent the news from leaking out.

She told 'The Late Show With David Letterman' last night (19.11.12): ''You can't really keep [a wedding] a secret, but we wanted to keep most of it a secret, at least up until it actually happened. So I kind of got quite obsessed with this CIA operative scheme I put in play right before the wedding.''

The 30-year-old beauty revealed she tried to confuse people about their wedding location by sneaking off on a pre-wedding spa retreat in an ''obscure Alpine lodge in Austria''.

But she said the trip didn't turn out to be as relaxing as she had planned because she ended up sharing a sauna with two naked men.

She said: ''We're in the spa, in the sauna, and in walk two husky Austrian men. I didn't really quite know what the protocol was, so I just laid there, frozen in my bikini and my robe and my towel and my slippers...And they drop their towels -- and they are butt naked. Older, husky men. They were naked! And I'm in the middle of them.

''It got worse from there. I look over, and I realise, yes, it is confirmed - there are balls on wood. I mean, not just naked, but balls on wood, Dave!

''I was so stunned. I was having this internal conniption. I just laid there...sandwiched in between [them].

''We found out later it was actually very normal. Some places in Europe, the spas are co-ed and nudity is cool.''