GeoPandas spatial index - passing RTree parameters to index

I am quite familiar how to work with the Toblerity RTree library:

import fiona
import rtree

with fiona.open(input_path,'r') as source:   
    p = rtree.index.Property()
    p.filename = "index.idx"
    p.overwrite = False
    p.fill_factor=0.6 # some - absurd  - values for tunning the index
    p.get_pagesize=20 # another absurd value, for demo purposes   
    index = rtree.index.Index(properties=p) #create index
    for f in source:
        ... # process features, add to index etc

I am, however, wondering, how to pass parameters to an index when calling the Geopandas sindex on a GeoDataFrame:

gpd.sindex 

does not take any arguments.

The documentation states that all parameters from RTree are supported, but I am unsure how to pass them to the sindex.