The speckled pup has the same mischievous streak as Old Yeller did.  He is naughty but endearing, as he demonstrates when he steals food from the family's table.

When Lisbeth gave Travis the dog, she said "He's part Old Yeller", but Travis had been too depressed and angry over Yeller's death to care.  His feelings of despondence continued for weeks, until an incident that happened one night at dinnertime. The speckled pup snuck into the kitchen and snatched "a big chunk of conbread...he raced around the house...yelling and squawling like somebody was beathing him to death, but that still didn't keep him from hanging onto that piece of cornbread that he'd stolen" (Chapter 16).  The incident reminded Travis of the first time he saw Old Yeller, who just showed up one day and stole the only side of meat that remained from the previous winter's hog butchering.  Without even acting ashamed, the dog "came romping toward (Travis), wiggling that stub tail and yelling "Yow! Yow! Yow! Just like he belonged there and (Travis) was his best friend" (Chapter 1).  The speckled pup apparently had the same thieving but lovable nature as Old Yeller, and the fact that Travis can appreciate this indicates that he is getting over the trauma of his beloved dog's death.