in all honesty, accardo should never, ever be mentioned in the same breath as Moe giancana. Accardo never held the absolute top spot in the outfit, he was always a front boss & consigliere. It's not that he wasn't good enough, he just didn't have that temperament and didn't want to sit on top. When giancana, was boss, he was boss. Ricca had the final say on things, but adored moe and trusted him. Back during the Moe reign, it was Ricca/Giancana vs. Accardo/Cerone, so basically Taylor st. vs. Grand ave, and its quite obvious who the more powerful crew was. Moe giancana honestly thought very poorly of aiuppa/Cerone/accardo. Also, aiuppa & Cerone were the ones that masterminded the Giancana murder plot. Aiuppa/Cerone ran the outfit from the time Milwaukee Phil passed to the time of the Vegas trial. Take a look at the family secrets dinner photo and Obrien is seated at the head of the table. Accardo was consigliere at best during those years.

anyways just thought I would add, cheers.