Even a bit of possessiveness can enhance your relationship to the next level... after all, you are possessive about your partner, for the only reason of staying together and your importance in other's life not being taken over by any other... but, anything in too much, even love, will spoil the relationship, so is possessiveness, if it crosses the limit... the only way you can control your possessiveness from crossing a limit is when you know what is that 'limit'...
Jealousy that crosses your thoughts and rules your mind is definitely to be curbed... it is okay to get a bit jealous if your partner is praising somebody else as a part of conversation or just like that... you can always present that you are jealous, on a lighter note, by cracking a joke, rather than portraying your angry self and not letting your partner expressing all those expressions with you, from the next time... think at this, this is even more dangerous... so, just learn taking things at a lighter note... if your partner is best friends with opposite sex, meets them in a group or even individually, talks over phone or praises, it is okay if it is not regular... but, by any chance, you are sensing this to be getting a little over board, don't forget to just express your feeling to your partner...
Not only possessiveness but even the nagging nature of yours will mess up your relationship for sure... just cut shot the argument and discuss to the point... if the argument is taking a worst turn, then prefer not to discuss at that moment and give a break... your thought of getting the issues solved then and there as if there is no tomorrow will worsen the situation but will help you in no way...
Just remember, only 'love' should blossom in your relationship and not any hatred and possessiveness...