Thanks for your comment, Nina. If you have access to a PTS edition of the Pali canon, I give book and page reference below so that you know which passage Frank referred to.
If I understood Frank correctly, his question involves the compound 'arittajjhaano' (not devoid of jhaana) in the stock phrase "Arittajjhaano viharati satthusaasanakaro ovaadapatikaro amogha.m ra.t.thapi.n.da.m bhu~njati" in Jhaana-vagga of AN volume I (AN I 38-43). Here the Buddha said that a monk who pursues/develops any of the following practices, even for a brief moment, is called 'a monk who is not devoid of jhaana, who acts upon the teaching of the Teacher, who responds to his advice, who does not eat the country's almsfood in vain.' The practices mentioned are: any level of the four jhaanas, mettaa cetovimutti or else upto upekkkhaa cetovimutti, any of the four foundations of mindfulness, chanda and viriya in regard to any of the four padhaanas (sa.mvara-padhaana, pahaana-padhaana, bhaavanaa-padhaana and anurakkhanaa-padhaana), etc.
The same expression is found in AN I 10-11, where the same is said for a monk who pursues/develops metta-citta.
You can find these in Syamra.t.tha edition vol. 20 p. 20 and pp.50-55 and in MMR Thai translation of Pali canon and commentaries book 32 pp.106-107 and book 33, pp.214-219.
Frank asked whether all those practices can be considered 'jhaana' as expressed by the compound 'arittajjhaano.' (Frank, please correct me if I misunderstood your question.) My answer was that probably the term 'jhaana' in the compound refers, not directly to those practices, but to the level of necessary concentration associated with those practices.
Here, I think the right view is already assumed, and the practices already right-practices. Otherwise the Buddha would not have praised the practitioner (monk) who pursues such practices as "satthu saasanakaro ovaadapatikaro amogha.m ra.t.thapi.n.da.m bhu~njati"