I used Stevens International after reading how great they were on several websites, and I found their service to be absolutely terrible. I was told it would take 6-8 weeks to receive my items, and it took just over 5 months! I know other people have had positive experiences with them, but I definitely didn't.
They sent a local moving company to handle the packing, and everything was fine with that. The woman that handled the scheduling was very friendly. I was told by Stevens International that my items would leave out of Los Angeles/Long Beach, but when I contacted them after 2 months, enquiring about the location of my items, I was told everything was sitting in their warehouse near the Port of Houston. They claimed there were no shipping containers available for my shipment. I worked in logistics, so I understand how international shipping works, and had booked my move 2 months before I left, so I didn't understand how they hadn't arranged a spot for my belongings in a shared container beforehand and how they hadn't found space in the past 2 months for my belongings. I kept asking about every 2 weeks where my belongings were, and they kept saying there were no containers available. FINALLY after over 4 months, they told me my belongings were on a ship. If they had taken any longer, they would have been in Houston for a huge hurricane, and apparently the area around where my items were being stored was flooded. They didn't tell me when my items arrived or when they cleared customs, ignoring my emails (probably annoyed with me after I had emailed them so frequently, but I was VERY annoyed with them), and I was only given a day's notice that my items would be delivered. They didn't tell me anything about what I needed to do to prepare for the shipment. I did tell them how difficult it would be if a large truck was sent, though. I lived in the middle of Edinburgh on a tiny street, and as I had very few items, I assumed they'd send a van instead of a full-sized truck. Well, there was a full sized truck that couldn't even get down my street, so my husband had to carry everything around the block. The movers refused to help, as they claimed I hadn't informed anyone that the truck couldn't make it down the street. My boxes were completely smashed, but luckily only a few Ikea plates were broken.
I'll never move a large shipment ever again, after that experience!