America's shale formations, in combination with new oil and gas recovery methods, have resulted in a new oil rush, and investors are eager to cash in on the prosperity. Luckily the energy sector is one of the few undervalued areas in this overheated market. The following three investments represent an exceptional way for long-term income investors to not only secure safe double-digit yields but also set the stage for above-average capital gains in the years ahead.

Linn Energy (NASDAQ:LINE) and Linn Co (NASDAQ:LNCO) are two sides of the same coin. Linn Energy is an MLP while Linn Co is a traditional corporation structured as a holding corporation for units of the MLP. The distributions of Linn Energy are what pay the dividends of Linn Co. The reason for this odd setup is that MLPs have inherent tax benefits but also tax preparation headaches. Both investments share the same assets and investment thesis.

Linn Energy is the largest independent E&P (exploration and production) MLP in America. It achieved its immense scale through a track record of disciplined and well executed accretive acquisitions (60 since its 2006 IPO, worth a total $15 billion). The investment thesis for this partnership (and Linn Co) is composed of two parts.

First, the price has recently taken a pounding due to allegations by Barron's magazine that the company has been misrepresenting its expense accounting. These allegations are being investigated by the SEC and are likely to be found false but the sharp drop in unit/share price has badly hurt the company. 

Its most recent (and by far largest) acquisition of Berry Petroleum was  done with Linn Co shares. The original terms of the deal were 1.25 Linn Co shares/share of Berry Petroleum. Due to the price drop (as well as price increase of Berry due to a record quarterly report), management was forced to increase the offer to 1.68 shares and the total cost rose to $4.6 billion. This threatened the accretive nature of the acquisition and created one additional problem for the partnership/company.

Berry Petroleum increased Linn's production by 30% (and doubled oil production). Oil is a much less volatile commodity than natural gas and so Berry's oil-rich Permian assets were a great addition to Linn Energy's portfolio. However, to increase production further would require expensive horizontal drilling and with the cost of the acquisition already greatly increased, management was forced to cut distribution coverage guidance for 2014 to 1. The market, fearful of an insecure distribution (10.4% yield for Linn Co, 10% Linn Energy), has deeply discounted Linn Energy (now trading at a 27% discount to the value of future cash flows from its oil/gas in the ground). However, the concern over the security of the distribution is overblown for three primary reasons.

First, management is guiding for 3%-4% organic growth in production while cutting capital expenditure (capex) by 11%. This will improve cash flows and strengthen distribution security.

Next, management is always on the look out for accretive acquisitions (which immediately improve distributable cash flow/unit). In 2014 alone, management has screened 48 potential purchases and bid on six (worth $5.5 billion).

Accretive acquisitions are likely in 2014 given the partnership's acceleration in recent acquisitions ($11 billion since 2010). Such acquisitions will further secure the distribution.

Finally management is exploring options to sell/trade some of its Midland basin assets (that would require expensive drilling to bring online) for assets that are already producing oil/gas. This would be immediately accretive to DCF and lower overall production costs for 2014, further improving distribution security. 

Breitburn Energy Partners (NASDAQ:BBEP) is another undervalued E&P MLP. A large impairment charge in the last quarter coupled with severe weather resulted in its distribution coverage ratio declining to 0.93, making the market nervous about the security of its high yield. Once more, I believe these fears to be overblown due to two factors. 

First, management is guiding for 36% EBITDA growth on the back of 27.5% production increases from its most recent acquisitions. This production is aggressively hedged at very favorable rates (76% of 2014 production hedged at $93.7/barrel oil, $4.95/Mbtu gas). This ensures high and predictable cash flow from which to pay the 9.8% distribution.

Second, management is guiding for $600 million in accretive acquisitions in 2014 (on top of $1.2 billion in 2013). Last year's acquisitions increased the partnership's oil exposure and future purchases are likely to be similar.

The combination of surging EBITDA and accretive acquisitions means that the distribution is not only safe, but likely to grow at its historic 3%-4% CAGR (2013 growth of 4.8%).

Foolish takeaway
A principle of Foolish investing is to buy quality companies with promising futures during short-term hiccups in the growth story and when they are most hated by the market. With Breitburn Energy Partners, Linn Energy, and Linn Co, investors have a chance to cash in on America's energy renaissance and secure both high (and growing) yields.

3 stock picks to ride America's energy bonanza
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Adam Galas has no position in any stocks mentioned. The Motley Fool recommends BreitBurn Energy Partners L.P.. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.