Self-managed superannuation funds (SMSFs) are a wonderful way to invest for high dividend yields because of how they are offer lower tax rates (perhaps 0% in retirement) for Australians.
But, in my view, I don't think every high-yield ASX share is a buy just because it offers a large near-term (or historic) yield. There are other aspects I want to see from an investment that may look appealing on the income side of things.

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Passive income stability
For me, it's very important that investors can rely on the passive income that they expect to receive.
I don't think there's much appeal to owning a business for dividends if that payout disappears when an economic downturn comes.
High yields are only attractive if those payments continue to flow, not just at certain times of the economic cycle.
For example, if I relied on dividend income to pay for my life expenditure, I wouldn't expect Fortescue Ltd (ASX: FMG) or Rio Tinto Ltd (ASX: RIO) dividends to remain as strong as they are now given how volatile mining earnings can be.
Underlying business and payout growth
Ideally, I only want to invest in businesses with attractive, long-term futures. Therefore, I only want to choose investments that I foresee delivering long-term capital growth due to profit growth and/or balance sheet growth.
The longer an SMSF (or anyone) holds an investment, the more time it has to deliver pleasing compounding.
If a business isn't improving its underlying value, then it may become harder for that business to maintain/grow its payout.
Owning businesses with rising payouts allows us to feel progressively wealthier as larger dividends arrive at our bank accounts.
ASX shares I'd buy in a SMSF with a dividend yield of more than 7%
There are not too many businesses on the ASX that tick the boxes of what I'm suggesting would suit well for an SMSF.
I'll highlight a few names that really stand out to me.
WCM Global Growth Ltd (ASX: WQG) is a listed investment company (LIC) that invests in a global portfolio of appealing businesses with growing economic moats and a company culture that helps improve the competitive advantages. Its forward grossed-up dividend yield is expected to be 7.25%, including franking credits. It has grown its annual payout each year since 2019.
Future Generation Australia Ltd (ASX: FGX) is another LIC, which donates 1% of its net assets to youth charities as fund managers work for free to enable that donation. Future Generation Australia's 2025 annual dividend translates into a grossed-up dividend yield of 7.8%, including franking credits. It has hiked its payout every year since 2016.
Charter Hall Long WALE REIT (ASX: CLW) is a diversified property owner which leases various types of properties on long-term leases, providing significant rental security. It's expecting to grow its FY26 distribution by 2% in FY26, translating into a forward distribution yield of 7.2%. At the current valuations, I think each of the above ideas can be a strong SMSF pick for a high dividend yield.