Opiates like codeine (hydrocodone and oxycodone) are usually compounded
with another medicine, like the acetaminophen you mentioned, but also
with aspirin. Among the medicines that codeine is mixed with aspirin are Lortab and Percodan, and they are short-acting. Opiates like morphine (hydromorphone) that are not compounded include the drug Dilaudid.
Some other analgesics without Tylenol include Darvon and Ultram or Tramadol.