I think some of the best ASX shares to buy are those that can deliver excellent long-term returns through powerful compounding.
When earnings grow at a strong compound annual growth rate (CAGR), it means the underlying intrinsic value is improving rapidly and does so for a long time.
I believe the following two names are excellent ideas for the decade ahead.

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Lovisa Holdings Ltd (ASX: LOV)
Lovisa is a global retailer of affordable jeweller around the world.
It has at least five stores in Australia, New Zealand, Singapore, Malaysia, Hong Kong, South Africa, the UK, Ireland, Spain, France, Germany, Belgium, the Netherlands, Austria, Switzerland, Poland, Italy, the UAE, the USA, Canada, Mexico, its Middle East and Africa franchise and its South America franchise.
The ASX share's expanding global store network is a key driver of the company's financial progress. In FY26 alone, its store count increased by 10.2% (or 105 stores) year-over-year to 1,136.
Revenue growth at its store network helped revenue grow by 17.6% to $938.8 million, underlying operating profit (EBITDA) rose 20.9% and net profit after tax (NPAT) increased 10.7% (despite all of the investing in new stores globally).
With so many markets it can grow in, including new markets like China, Vietnam, Taiwan, I think the business has a very promising future of expansion in the decade ahead. Operating leverage could help improve its profit margins over time.
According to the forecast on CMC Invest, the Lovisa share price is valued at 19x FY28's estimated earnings.
Siteminder Ltd (ASX: SDR)
Siteminder is one of the world's leading hotel commerce and management software providers. The business generates 140 million hotel reservations worth over A$85 billion in revenue for its hotel customers.
In an increasingly digital world, the ASX share is seeing strong adoption around the world.
In FY26, Siteminder reported that revenue grew 18.6% to $266.1 million and annual recurring revenue (ARR) improved 14.9% to $313.7 million, despite softer global travel conditions.
It's benefiting from growing traction in new product initiatives, such as its smart platform modules that help customers analyse financial performance, decide on room prices, and even automatically adjust them so customers can generate the most revenue over the year.
In terms of profitability, the nature of software means revenue can rise much faster than expenses.
While the ASX share's revenue grew 18.6% in FY26, underlying operating profit (EBITDA) jumped 96.5% to $28.1 million, and adjusted free cash flow surged 123% to $10.5 million. I expect its profit margins will continue to improve in the years ahead, although they are unlikely to do so at the same pace as in FY26.
According to the projection on CMC Invest, the Siteminder share price is valued at under 30x FY28's estimated earnings.