  Sliding suffix trees (Fiala & Greene, 1989) for an input text $T$ over an
alphabet of size $\sigma$ and a sliding window $W$ of $T$ can be maintained in
$O(|T| \log \sigma)$ time and $O(|W|)$ space. The two previous approaches that
achieve this can be categorized into the credit-based approach of Fiala and
Greene (1989) and Larsson (1996, 1999), or the batch-based approach proposed by
Senft (2005). Brodnik and Jekovec (2018) showed that the sliding suffix tree
can be supplemented with leaf pointers in order to find all occurrences of an
online query pattern in the current window, and that leaf pointers can be
maintained by credit-based arguments as well. The main difficulty in the
credit-based approach is in the maintenance of index-pairs that represent each
edge. In this paper, we show that valid edge index-pairs can be derived in
constant time from leaf pointers, thus reducing the maintenance of edge
index-pairs to the maintenance of leaf pointers. We further propose a new
simple method that maintains leaf pointers without using credit-based
arguments. The lack of credit-based arguments allow a simpler proof of
correctness compared to the credit-based approach, whose analyses were
initially flawed (Senft 2005). In addition, our method reduces the worst-case
time of leaf pointer and edge label maintenance per leaf insertion and deletion
from $\Theta(|W|)$ time to $O(1)$ time.
