Mark Duggan's family has urged judges to overturn an "unsafe" lawful killing inquest verdict delivered in 2014.
The 29-year-old was fatally shot by a police marksman in north London and his death sparked riots in Tottenham that spread nationwide in August 2011.
Hugh Southey QC said the coroner had given the jury an "unlawful direction" which made the original verdict unsafe.
The Court of Appeal judges have reserved judgement in the case and will announce the ruling at a future date.
Addressing the three Court of Appeal judges earlier, Mr Southey QC said: "No verdict is better than one based on an unlawful direction."
He said it was important to the family that the previous unlawful killing verdict be overturned and for it to be recorded as unsafe.
An inquest jury previously concluded by a majority of eight to two that Mr Duggan had lawfully been killed by armed police.
His aunt, Carole Duggan, has always maintained the death was an execution.
No gun was ever found on Mr Duggan but a weapon was discovered about 20ft (6m) away from where he died.
No date has yet been set for the Court of Appeal ruling.