While all three compact SUVs are impressive in their own separate ways, your best bet here is the Skoda Kylaq. Its 1.0 TSI engine and 6-speed automatic combination is smooth, which should come in handy around town. It's also very spacious and comfortable, and even quite a lot of fun to drive. When you go out on the highway, it's reassuringly stable and rides comfortably, too. 

The Mahindra XUV 3XO has many of these traits too, but its engine, while powerful, isn't as smooth, refined or efficient as the Skoda's, and it has a tiny boot. The Sonet is starting to show its age, and its rear seat is very cramped. Plus, around town, its DCT gearbox can be quite jerky, and ride quality is firm too.

The Maruti Suzuki Brezza AT VXI is a sensible choice, though it's a bit out of your budget. The Brezza isn't exciting to drive, but it delivers reasonable performance and fuel economy and also scores well for ride comfort. The cabin is also practical and roomy. 

If you want something more exciting, you have the option of the Mahindra XUV 3XO Petrol AT MX3, the Skoda Kylaq AT Signature, and the Maruti Suzuki Fronx Turbo AT Zeta. The 3XO feels strong and offers the most room for five passengers, if that's a requirement. 

The Skoda Kylaq is most enjoyable to drive thanks to its fun handling and punchy engine. Maruti's Fronx Turbo strikes a good balance between performance and fuel economy.  

There are only two options that would meet your requirements of a diesel automatic and under Rs 13 lakhs. These are the Mahindra XUV 3XO and the Tata Nexon. It would be nice to know a bit more about your requirements to pinpoint one. 

The Tata Nexon is a good option, as fuel efficiency is very important for you, as its efficiency is higher than the 3XO. In our real-world tests, we got an average of 18kpl for the Nexon and 15.5kpl for the Mahindra. 

If, however, driving pleasure and interior space are important, then you would be better off in the 3XO. The engine is refined and delivers good performance. Also, the car is spacious from inside, especially at the rear, where you will find more passenger room than in the Nexon. 

If you like the Hyundai Venue 1.0 Turbo DCT, go for it. It is a thoroughly modern, spacious and feature-rich compact SUV. The powertrain has ample performance, and it drives nicely, too. The dual-clutch automatic can feel a bit jerky in bumper-to-bumper traffic, hence we'd recommend you opt for an SUV with a torque converter automatic instead. 

The Mahindra XUV 3XO 1.2 MPFI Turbo petrol AT is an option you must seriously consider. It has a stronger engine and a smoother transmission, which feels more suited for stop-and-go conditions.

• Maruti Suzuki Brezza ZXI AT: Down on wow features to the Venue, but has a smoother gearbox, plusher ride, and more comfortable seats.
• Skoda Kylaq Signature+ AT: Again, not as well-equipped as the Venue, but it has a smoother gearbox and punchier engine. Space at the back is less, but it shouldn't be a deal breaker for you.
• Kia Sonet HTX Petrol DCT: It is due for replacement within a year, but it is very competent. Packs in plenty of tech and shares its engine and gearbox with the Venue, and is actually a better value for money. Space is less at the back, but it shouldn't be a deal breaker for you.
• Mahindra XUV 3XO REVX A: Stronger engine, lots of features, and feels tougher in its build. Boot space is less than the Hyundai car.

The Kia Carens Clavis is the ideal pick for your requirements. It's a well-packaged MPV that offers comfortable seating across all three rows. A one-touch operation for the middle row seat fold makes access to the last row easy. Also, there is ample movement built into the middle row to balance space for all passengers. 

The Clavis is also easy to drive and doesn't intimidate as some three-row SUVs can. From the Clavis line-up, the Turbo DCT HTX(O) is the one to buy.

Of the other three-row petrol-auto options, there's the Hyundai Alcazar, MG Hector Plus, Mahindra XUV 7XO and Tata Safari.

Both the Tata Nexon and Mahindra 3XO are tough-feeling and robust compact SUVs, and both boast 5-star Global NCAP safety ratings. Both models also get branded audio systems, though it's advisable to test them out for your preferences. 

Of the two models, it's the Mahindra 3XO that's the more complete package. It's better finished, better equipped and more spacious than the Tata Nexon. What also tips the ratings in favour of the Mahindra is its punchier petrol engine and slicker gearboxes - both manual and automatic. 

Where the 3XO loses out is in luggage capacity, offering less room than you'd get in a Nexon.