There are two ways that tougher crime measures may aggravate crime rates. The first is by extending the range of things deemed criminal behaviour. For example, in the UK the government (inspired to an extent by the US in its approach to crime fighting- even hiring US cops to head schemes) is introducing anti-social behaviour crimes, and has also criminalised things like grooming over the internet. I'm not saying that these things are necessarily wrong policies, but part of becoming tough on crime means criminalising behaviours previously a matter of civic concern. This widens the remit of law enforcement and means more cases, more trials, moer prisoners.
Second, comes the reciprocal spiralling of crime that occurs when crime fighting becoms tougher. Again to use the UK as an example, gun crime is rising in the UK, and whilst regular police are not armed, the armed response units that offer back up to unarmed cops are being used more and more frequently. So the debate is heating up about whether or not to arm our cops (most people and cops themselves aren't that eager to do this, and even those in favour aren't champing at the bit, and come across as rather disappointed that this may be the future). One argument against is that if determined criminals know that cops are going to be armed, they will tool up more frequently as well, and you'll get a cycle of escalation of the severity of crimes committed. Indeed, one of the arguments against armed police in the UK is the fear that we will descend into the kind gun culture of the USA with everyone shooting at everyone else (cops, criminals and civilians). Recently in the UK they've started using tasers and pepper sprays and still use rubber bullets (although no one calls them that anymore, after dozens of people have been killed over the years when they've been used in Northern Ireland). Incidentally has anyone else noticed the way that the producers of these devices and police users have changed their name from 'non-lethal weapons' to 'less lethal weapons' in a very overt acknowledgement that these things can and do kill people.
There is another aspect to tirades about rising crime as well, and that is the new opportunities for new kinds of crime, obviously a whole range of new crimes made possible through the internet that didn't exist 15 to 20 years ago, or mobile phone thefts etc. etc. One thing in the press currently is the RIAA's ridiculous attempts to prosecute MP3 file-sharing for breach of copyright, a principle that has applied to music only for an astonishingly small part of its history (recall the days before pre-recorded music when musicians made a living by actually going around playing their music, and allowing others to play their music).