Baby won't sleep alone

Here's the thing... Before having this baby I was 100% against bed sharing with babies because I have had to investigate many infant deaths caused by bed sharing. Typically, the cases I worked involved the baby suffocating while sharing a bed with parents or siblings. The families were all good loving families, never under the influence of drugs, just normal parents sleeping in bed with their infants. So because of this, I vowed to never allow my infant to sleep in bed with us and follow all the safe sleep rules. Well, fast forward to now. I have a 3 week old baby boy who will not stay asleep unless I hold him, or he's next to me, or he's in his swing. If I put him in his bassinet next to our bed, he will only sleep for a very short amount of time. I need a compromise! I need a safe place for him to sleep. I have let him sleep next to me in bed, but I didn't sleep because I was so worried. I won't let him sleep in his swing without supervision because his head falls after a while and I'm worried that could make breathing difficult for him. Any suggestions on what I can do to help us both get some sleep but keep him safe?