Why is IE not storing my Cookie?

I'm developing a (J2EE) website, and the cookies it sends are being persisted on Chrome and Firefox, but not IE. I've even set IE up to 'allow all cookies', but the ones from my site are not being persisted. Google, Twitter etc, cookies do get persisted.

Using Fiddler for IE, I see that my login page is correctly sending a cookie:

Response sent 65 bytes of Cookie data:
Set-Cookie: JSESSIONID=1C5C8622CEC9338714F72A3CBFB5DDF8; Path=/tms/; HttpOnly

Response sent 132 bytes of Cookie data:
Set-Cookie: tms-remember-me=superuser; Version=1; Domain=""; Max-Age=31536000; Expires=Sat, 03-Jun-2017 01:40:21 GMT; Path="; HttpOnly;"; Secure

This response did not contain a P3P Header.

Validate P3P Policies at: http://www.w3.org/P3P/validator.html
Lea more at: http://fiddler2.com/r/?p3pinfo

Is the reason IE is not persisting this cookie likely to be the absence of a P3P header? Is there anything else about the above cookie that may cause IE to reject it?

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