The teaching of native-like accents has been the aim of many EFL educationists long ago; however, this concept is heading towards a major change. Hence, the idea of this paper is based on Jenkins' (2000 & 2002) theory of English as an International Language (EIL). Jenkins' theory analyses the use of English by non-natives speakers (NNS) where the interlocutor is also a NNS; and hence designs a Lingua Franca Core (LFC), that she proposes as a foundation of EIL courses. This study attempted to apply LFC in an EIL classroom in the College of Basic Education in Kuwait, with English major students who are either taking part in a conversation class or a phonetics class. The researcher first selected parts of LFC applicable in the Kuwaiti context, in terms of consonants, vowels, word/syllable stress and connected speech. This choice was based on six hours interaction with both groups. The students were given a questionnaire investigating students' preferences and reflection of the use of Kuwaiti-English exercise tapes and had a group in-class discussion. After the analysis of the questionnaire feedback, the author found that the majority of students would prefer to be exposed to RP or GA, yet be free to use their own Kuwaiti-English dialect. The author later proposes a method of working with the students' abilities and preferences.