We study two particular modifications of the P-property of ideals and related cardinal invariants cofđ„ (â)and cov+(â). We give some results on the existence of P (đ„)-ideals or non-P (đ„)-ideals regarding specific classes of ideals, particularly meager ideals on Ï. We also provide values of the cardinal invariant cofđ„ (â) describing the smallest families ensuring P(đ„) for particular critical ideals. Moreover, we obtain a simple way of proving strict inequalities Fin <K ăđ ă <K Fin Ă Fin for any MAD family đ using the weak P-ideal notion.