Oil and gas prices are down sharply from their peaks, even after the recent Saudi-driven boost. Because of that, many energy stocks have lost altitude. That's driven their already high dividend yields even higher.

Three energy stocks currently offering big-time payouts due in part to the dip in their stock prices in recent months are Crestwood Equity Partners (CEQP), Enbridge (ENB 0.14%), and Pioneer Natural Resources (PXD -0.62%). With energy markets likely to improve following the Saudi move, they look like great stocks to buy on the dip for those seeking big-time yields and upside potential.

1. The massive payout is growing more sustainable

Units of Crestwood Equity Partners have slumped about 20% over the past year. That has pushed the master limited partnership's (MLP) distribution yield up over 10%. 

The company can easily afford that big-time payout. It expects to generate $430 million to $510 million of distributable cash flow this year, covering its distribution by 1.6 to 1.8 times. Meanwhile, it will produce enough excess cash to fund its expansion-related spending with $10 million to $90 million to spare. That will give it additional funds to reduce debt. 

The company already had a solid balance sheet. However, it wants to have even more future financial flexibility by getting its debt-to-earnings before interest, taxes, depreciation, and amortization (EBITDA) ratio below 3.5 times. It expects to end this year in the 3.7 to 4.1 times range. Achieving its long-term leverage target would put its monster payout on an even more sustainable long-term foundation.    

2. Plenty of fuel to keep growing the big-time payout

Enbridge's stock price has slumped about 17% from its 52-week high. That's helped drive its dividend yield up to 6.8%.

The energy infrastructure giant backs that payout with a rock-solid financial foundation. It has a relatively conservative dividend payout ratio of 60% to 70%% of its distributable cash flow. Meanwhile, it has a strong investment-grade balance sheet, with leverage currently around 4.7 times, putting it toward the low end of its 4.5 to 5.0 times target.

That financial profile gives it billions of dollars of annual investment capacity to fund its continued expansion. The company has a multibillion-dollar capital project backlog under construction that should drive growth for the next several years. Meanwhile, it has several more projects under development. They should give Enbridge the fuel to continue growing its dividend for years to come.

3. The potential to pay a gusher of dividends if oil keeps rising

Shares of Pioneer Natural Resources have plunged about 27% from their 52-week high. The primary factor weighing on the stock has been a decline in oil prices. That will impact the oil and gas producer's cash flow.

It will also affect its dividend payments because Pioneer has a fixed-plus-variable payout policy. The company pays a fixed base dividend each quarter. In addition, it pays out up to 75% of its quarterly free cash flows via variable dividends. Because of that, it can pay a gusher of dividends as oil prices rise.

For example, at $80 a barrel -- right around the current level following Saudi Arabia's production cut -- Pioneer estimates it can pay out $20 per share in dividends each year. With the share price recently around $210, Pioneer could pay a dividend yield approaching 10%. Meanwhile, that lucrative payout will rise with oil prices.

Attractive income and upside opportunities

Falling oil prices over the past year have put downward pressure on valuations across the oil patch. Because of that, investors can grab some pretty enticing dividend yields from companies with lots of upside potential from a rebound. Crestwood Equity, Enbridge, and Pioneer Natural Resources offer loads of both, making them attractive energy stocks to buy on the dip.