Pitjantjatajra is an Australian language, part of the Greater Western Desert language dialect chain. In this study we focus on the lexical prosody of Pitjantjatjara, and show that the left edge of the word is primarily marked by a raising of pitch and by greater duration; greater spectral energy may also play a role, but vowel spectral tilt and vowel formant structure appear not to mark word-level prominence. There is no evidence for secondary stress, contra previous observations by non-native language researchers. These results are based on read text recordings of seven speakers, including two different texts. We suggest that non-native speakers of stress languages, such as English, may be susceptible to stress ghosting - hearing stress where there is no phonetic evidence of stress in another language. We discuss possible phonetic bases for such a stress ghosting, and conclude that the expectation of rhythmicity and secondary stress by speakers of languages such as English is the most likely reason for this illusion. This is yet another example of native language influence on non-native speech perception.