Wastepaper to China is, unfortunately, one of the biggest commodities the U.S. exports there. The very nature of the commodity means pretty cheap container rates. But it appears that could change with this announcement via CargoNewsAsia:
The Westbound Transpacific Stabilisation Agreement (WTSA), a discussion group of 10 carriers in the trade between the US and Asia, announced proposed rate increases of US$50 per 40-foot container and $40 per 20-foot container to take effect on September 1 for port-to-port as well as intermodal shipments.
As the article points out, these are proposed increases and purely voluntary, the lines are free to choose whether to implement them or not, but I would suggest that wastepaper exporters be prepared for some kind of an increase.