Claim 0 or 1 on W-4

My spouse claims 0 and I claim 1 on our Federal return (Married filing jointly.) We both work full-time, and have 2 children (18 and 17 years of age).  Each year we owe Federal and State taxes.  Besides increasing our 401K contributions, any advice on how to lower our tax burden through adjustments to our W-4’s?