This paper was also referred to in the one above about Chiquihuite Cave in Mexico's Zacatecas state:
Earliest Human Presence in North America Dated to the Last Glacial Maximum: New Radiocarbon Dates from Bluefish Caves, Canada

The Mexican site seems to be on a par with a Canadian site age-wise. From the Bluefish paper:

Introduction
Beringia, a vast region stretching from the Lena River in Siberia to the Mackenzie River in the Yukon Territory [1, 2], is thought to have played a pivotal role in the initial dispersal of human populations from Asia to North America. The exact timing of the initial dispersal remains uncertain, however. Recent genetic and palaeogenetic analyses [3–10], as well as dental morphological evidence [11], confirm that human populations migrating into North America originated in Siberia. They also suggest that dispersing groups reached Beringia during the LGM (dated to ca. 18,000–24,000 cal BP) where they were genetically isolated for up to 8,000 years before moving south of the ice-sheets into North America [3–11]. Unfortunately, archaeological support for the standstill hypothesis is scarce [12]. Recent archaeological discoveries prove that humans were able to adapt to high-latitude, Arctic environments by at least 45,000 cal BP [13]. The Yana River sites, in Siberia, demonstrate that modern human populations had reached Western Beringia by 32,000 cal BP [14, 15], i.e., well before the LGM. Human activity is not recorded again in Western Beringia until the post-LGM period, however, with occupations of two open-air sites, Berelekh and Ushki, dated to ca. 14–13,000 cal BP [16–18]. In Eastern Beringia, the oldest currently accepted human occupations occur in the Tanana valley (interior Alaska) at Swan Point, Broken Mammoth and Mead [19–21], and at the Little John site, located 2 km east of the international border in the Yukon Territory [22]; these sites are no older than ca. 14,000 cal BP, however [19–22]. The only potential candidate for an earlier, LGM occupation of Beringia is the controversial Bluefish Caves site.

Excavated from 1977 to 1987 under the direction of Jacques Cinq-Mars (Archaeological Survey of Canada), the Bluefish Caves site (northern Yukon Territory, 67°09’N 140°45’W) occupies a unique place in Eastern Beringian prehistory. The site is comprised of three small karstic cavities, not exceeding 30 m3 in volume, located in the Keele range about 54 kilometres southwest of Old Crow village. The caves are situated at the base of a limestone ridge about 250 meters above the right bank of the Bluefish River [23–27]. All three cavities contain a loess layer (Unit B) up to one meter thick, deposited on bedrock (Unit A) and overlain by a humus layer mixed with cryoclastic debris (Unit C) and finally, a modern humus layer (Unit D) [25, 27]. The loess deposit (Unit B) can be differentiated into three sub-layers based on granulometric and sedimentological examinations and was excavated in 5 cm spits [23]. Small artefact series were excavated from the loess in Cave I (MgVo-1) and Cave II (MgVo-2) and rich faunal assemblages were recovered from all three caves [23–27]. The lithic assemblages (which number about one hundred specimens) include microblades, microblade cores, burins and burin spalls as well as small flakes and other lithic debris [23–26]. Most of the artefacts were recovered from the loess of Cave II at a depth comprised between about 30 to 155 cm. The deepest diagnostic pieces–a microblade core (B3.3.17), a burin (B3.6.1) and a core tablet (B4.16.4) found inside Cave II, as well as a microblade (E3.3.2) found near the cave entrance–derive from the basal loess at a depth of about 110 to 154 cm below datum, according to the CMH archives [28]. While the artefacts cannot be dated with precision [24, 25, 29], they are typologically similar to the Dyuktai culture which appears in Eastern Siberia about 16–15,000 cal BP, or possibly earlier, ca. 22–20,000 cal BP [30]. There are no reported hearth features [24]. Palaeoenvironmental evidence, including evidence of herbaceous tundra vegetation [31, 32] and vertebrate fauna typical of Pleistocene deposits found elsewhere in Eastern Beringia [27, 33, 34], is consistent with previously obtained radiocarbon dates which suggest that the loess layer was deposited between 10,000 and 25,000 14C BP (radiocarbon years Before Present), i.e., between 11,000 and 30,000 cal BP [23–27, 35] (Table 1).

And if you haven't flogged this topic enough, Wikipedia has an entry about the Mexican cave and the controversy.