Source: North Atlantic Drilling

The offshore drilling industry is in the midst of a deep downturn brought on by weak demand for drilling rigs made worse by falling oil prices. The downtown shows no signs of improving, with many in the industry expecting it to linger at least through the middle of 2016. That being said, the downturn is having a bit of a cleansing effect on the industry as companies scrap their older rigs. That should lead to a more balanced rig market, and improved market conditions, in a couple years.

With that turnaround not yet on the horizon, tough days are ahead. Some companies are better positioned for those hardships, including the three I believe are the best offshore drilling stocks to buy right now. However, there are three more offshore drilling stocks that I also believe have compelling upside, but that should remain on watch lists due to current conditions and their own specific issues.

1. Transocean Partners (NYSE:RIGP)
Transocean Partners is a growth-oriented limited liability company, which is similar to a master limited partnership, formed by Transocean (NYSE:RIG) to own and operate offshore drilling rigs. The company owns a 51% interest in three ultra-deepwater drilling rigs, with the remaining 49% owned by Transocean. That's a very small initial fleet, which is to be expected as Transocean Partners only went public last year. However, that small fleet and lack of track record are why I believe the company is only watch list-worthy at the moment. Investors will want to see a bit more visibility on future fleet growth, particularly on drop-downs from Transocean. Investors will also want to make sure Transocean Partners isn't overpaying its parent for rigs, as that could destroy value rather than create it.

2. North Atlantic Drilling (NYSE:NADL)
North Atlantic Drilling has some similarities to Transocean Partners in that it was created by its parent company, Seadrill (NYSE:SDRL), to further its growth. Specifically, it was created to own and operate rigs focused on drilling in the harsh North Sea environment. It owns eight vessels, six of which are under contract for most of this year. This company is worth watching because it has a major strategic alliance with Russian oil giant Rosneft for six offshore contracts worth $4.25 billion. At the moment, however, that deal is being delayed by the western sanctions against Russia, as well as by weaker oil prices. That said, if the deal does go through it would boost the value of North Atlantic Drilling.

3. Rowan (NYSE:RDC)
Over the past few years the offshore drilling industry has focused much of its attention on building two types of vessels: ultra-deepwater drillships and high-specification jack-ups. While Rowan has focused on both markets, it owns an industry-leading 19 high-spec jack-ups, which for perspective is five more than Seadrill and North Atlantic Drilling plan to have by 2018 (which would be the second-largest fleet). At the moment high-spec jack-ups aren't in high demand due to the downturn in the oil market. However, 37 jack-ups currently in use across the industry are more than 40 years old, and 289 that will reach that age over the next decade. As these older vessels are scrapped it will reduce the oversupply in the market, which should put Rowan's top-notch fleet in high demand.

Investor takeaway
The offshore drilling sector is a turbulent one for investors at the moment. However, the market has compelling long-term potential thanks to the world's growing need for oil. In time that demand should lead to more robust conditions in the offshore market, which should result in brighter futures for Transocean Partners, North Atlantic Drilling, and Rowan. Until that time, and until these companies deal with some specific issues, these stocks are best put on a watch list.