The US chemical safety board concluded in its report that the spill was a result of poor coordination of effort between BP and the contractor hired to do the drilling with their own drilling rig, not a BP rig. BP seems to have thought that since the job was contracted, their own main focus could be worker safety, ironic since eleven workers were killed in the explosion. What this implies is that the first thing BP and similar companies might do to contribute to oil spills is not to cause them (or to not cause them, if you don't mind a split infinitive).
Step one on this line would be to have the same standards for contractor owned equipment as for BP owned equipment. Co-chair of the US oil spill investigation, senator Bob Graham, FL, called this spilt standard "reprehensible," while Donald Winter, chair of the National Academy of Engineering investigation, pointed out that worker safety and rig system integrity are "fundamentally different" concerns. BP's second step would be to prioritize safety concerns correctly and to superintend rig safety themselves and not delegate rig safety to contractors.
As to after-the-fact doing more is harder to pinpoint according to BP, they spent $14 billion on their share of the clean up. While BP has deep pockets, one wonders if their pockets can really go much deeper than that without causing another disaster resulting in laying off employees and causing an economic "spill." Rather than after-the-fact increase in responsibility, I'd favor before-the-fact increased responsibility where public announcements of actions taken for supervision of contractors and for increased assurance of rig integrity (while not neglecting worker safety) are published next to the applicable government regulations, perhaps in Wall Street Journal. This might make watchdogs of the whole country.
BP Website Deepwater Horizon accident page: We have acted to take responsibility for the clean-up working under the direction of the federal government, to respond swiftly to compensate people affected by the impact of the accident, to look after the health, safety and welfare of the large number of residents and people who helped respond to the spill and to support the economic recovery of the Gulf Coast’s tourism and seafood industries impacted by the spill. As at 31 December 2011, we had spent $14 billion on our response activities. Throughout, we have sought to work closely with government, local residents, our shareholders, employees, the wider industry and the media. (BP)