A Tasmanian Magistrate has dismissed one of two charges of possessing child exploitation material being defended by Clarence City alderman, David Traynor.

The Magistrate's Court in Hobart has heard Traynor "went out of his way" to ensure the pornographic items he downloaded did not involve children.

53 year old Traynor, of Cremorne, has pleaded not guilty to two counts of possessing the material, after his stolen laptop was recovered by police.

In his police interview played to the Hobart Magistrate's Court this morning Traynor admits he searched for images of "younger females".

Traynor told police he "wasn't stupid" and only used sites claiming those depicted were over the age of consent.

The court heard there were 4,500 videos, 4,800 images and 25 stories of a pornographic nature recovered from Traynor's council-issued laptop.

Only two items - a cartoon strip and a 450 page fictional journal - depicted children engaged in sexual acts.

Traynor's lawyer, Bruce McTaggart, told the court when Traynor downloaded items containing children he deleted them.

Magistrate Michael Hill said while a computer expert may have been able to retrieve a deleted sexually explicit cartoon, Traynor did not have the skills to do that.

The hearing is continuing in the Magistrates Court.