Leicester finished the Pool stages with a comfortable win over Neath to guarantee themselves a home draw in the quarter-finals.
And the twice Heineken Cup champions sent a message to new tournament favourites Toulouse that this title is theirs, and they will not give up their favourite trophy without a fight as they taught Neath a lesson at a packed Welford Road.
A five try to one victory underlined the supremacy of the English side, a first-minute try from Ireland wing Geordan Murphy sounding warning bells for the travelling support.
And with Tim Stimpson pinning back Neath with an excellent display of kicking from hand, Neath spent almost the entire match on the back foot.
Pinpoint accuracy is Simpson's trademark, and his four penalty goals ensured Neath were punished for every mistake.
British and Irish Lions captain Martin Johnson was his usual rampaging self, and with the support of fellow Lion backrow man Neil Back, and future Lion legend Lewis Moody, the home pack were just too strong for their visitors.
When scrum-half Jamie Hamilton scored to give Leicester a 21-8 lead at the break, the Tigers were on cruise control.
Further five-pointers from Josh Kronfeld and Ben Kay in the second period put the result beyond doubt.
A try to Neath winger Shane Williams and six points to fly-half Shaun Connor prevented a whitewash, but Neath will be disappointed they didn't cause the Tigers more problems after pushing them so close in round one.