I tend to go overboard when wrapping things for shipping. It could just be I'm jinxed when it comes to having ridiculous things happen to my packages though.
What I would do, is after wrapping it in something that will protect theitem from picking up something from the wrapping materials (white tissue wrapping paper, unprinted brown craft paper are all probably good--never newspaper or something colored directly on your product--the ink rubs off onto everything during shipping), I'd grab a few plastic grocery sacks and wrap them around it and tape them down. Then, put it inside of a box that is just barely large enough, then use peanuts or air baggies to wedge it in there nice. Then tape the box up well. I always add a card at this point -- basically a copy of the mailing label that will be on the outside of the second box--and tape that on the box. Then I get a box that is at least 2" bigger all the way around, put peanuts or airbags to half-full, then cover with newspapers so it forms a "floor", and put the smaller box in and secure it with straps of tape in the the middle of the bigger box, Sometimes another layer of paper, then finish padding with peanuts and bags, and seal all the edges of the box with tape.
The two-box method really protects against drops and having other items fall and crush it during transit. The securing of the smaller box in the middle of the larger, making a newspaper floor, and strapping the inner box there keeps the smaller box from shifting from the middle and jiggling its way to the outside of the box where it won't be well protected. The label on the inner box will insure my package gets delivered even if the outer box is destroyed (and the padding in the inner box will protect it to some degree while it continues its journey). The plastic on the inside of the inner box protects against moisture if the shipper spills a coffee or large glass of sticky soda on the box, of the shipper delivers it in the rain, and/or/leaves it on the porch of someone's house in the rain.
It's a pain, but by doing this, I have successfully shipped boxes of fragile to fairly fragile items that at the end-point have been ripped open by a bored dog (inner package protected the product), been left in the rain, left by a mailbox and buried by a plow, been placed in a 4" deep mud puddle, been sat on, had coffee and soda spilled on them, been dropped, been mangled, been completely separated from the outer box, clawed by cats, kicked around the yard by the neighbor's kids, and so on. The most absurd thing that happened is when the shipper left the package by the gate at a rural location, and the cattle being grazed in the area on a grazing lease decided they liked the taste of it and ate the cardboard boxes (inner and outer), and all the packing peanuts... they weren't interested in the plastic bags, so the glass wind chimes were safe--and protected from the cow pat the buyer found on them when she got home from town. (ew).