There were several questions regarding Laghu Krama Diksha, and I attempt to answer the same below.
There are three ways to initiate a disciple:
महादीक्षा तथा दीक्षा उपदेशस्ततः परम् ||
Upadeśa is the least recommended but easiest of all, where a Guru gives upadeśa of a mantra to his disciple. This seems to be the most commonly followed method in Southern India especially among worshipers of Srīvidyā.
Dīkṣā refers to Pūrṇadīkṣā within a specific Mahāvidyā such as Srīvidyā which, for example, is taught variously by Tantras such as Paramānanda and Paraśurāma Kalpasūtra. This is considered madhyama or average.
Mahādīkṣā is known as Kramadīkṣā and involves various Mahāvidyās, with the primary focus on either Tripurasundarī or Kālikā. This can be taught only by a Siddha Guru.
There are three main Sampradāyas of Srīvidyā Krama Dīkṣā and they are:
1. Mahāmanthāna Bhairava Krama
2. Unmatta Bhairava Krama of Gauḍas (elaborated by Tantras such as Bṛhadbaḍabānala etc.)
3. Svacchanda Bhairava Krama (detailed in Tantras such as ūrdhvāmnāya Tantra, Shaḍanvaya Mahāratna etc. followed by our lineage)
Our lineage, traced back to Bhagavatī Bimbāmbikā, only teaches Pūrṇa Krama consisting of 360 mantras and there is no Laghu (brief) krama taught. However, The Unmatta Bhairavīya Krama does teach a laghu-krama, which seems to have been co-opted by some in my our lineage as well. For example, Muktakeśānandanātha, who authored the manual Nīlakālī Saparyā (centered around the Krama procedures for Nīlasarasvatī and Ucchiṣṭa Mahāgaṇapati) discusses Laghu-krama for Srīvidyā. Another medieval work, Upāmnāya Ratnakośa, dealing mainly with the vidhi for Triṣakti Chāmuṇḍā also known as Chaṇḍī colloquially and as Ugracaṇḍā in Krama system, also discusses this Laghu-krama of Unmatta Bhairava school.
सर्वाम्नाय प्रभेदेन षड्धा विद्याक्रमः स्मृतः |
The system detailed below is mainly for Kādi Srīvidyā. There are similar systems for Kālī that include both Kādi (Dakṣiṇā) and Hādi (ādyā). And for Tārā that include both Hādi (Nīlasarasvatī) and Sādi (Ugratārā & Ekajaṭā).
पूर्वाम्नाये चोन्मनी च पूर्णेशी भुवनेश्वरी |
द्वीपशाम्भवकं दिव्यं लिङ्गमूले व्यवस्थितम् ||
The deities of Purvāmnāya meditated upon in Svādhiṣthāna Chakra are: Unmanī, Pūrṇeśvarī, Bhuvaneśvarī and Dvīpeśvara – Dvīpeśvarī.
There are certain differences in opinion regarding Mūlādhāra, Svādhiṣṭhāna and the order of contemplation for Adharāmnāya and Pūrvāmnāya. Some lineages worship Bauddha deities such as āryatārā and Vajraprastāriṇī in the nether āmnāya whereas those such as mine propitiate Ugratārā. In any case, Laghu Krama does not include this lower āmnāya. A detailed discussion on this topic is quite irrelevant here.
आद्या श्यामा दक्षिणा च दक्षिणाम्नायवर्त्मनि |
संवर्तशाम्भवं दिव्यं मणिपूरे व्यवस्थितम् ||
The deities of Dakṣiṇāmnāya meditated upon in Maṇipūraka Chakra are: ādyā kālī, Shyāmā kālī, Dakṣiṇā kālī and Samvarteśvara – Saṃvarteśvarī.
पश्चिमे कुब्जिका वज्रकुब्जिकाऽघोरकुब्जिका |
सर्वाधिकारविद्याख्यं शाम्भवं चतुरन्वयम् ||
The deities of Paścimāmnāya meditated upon in Svādhiṣthāna Chakra are: Samayakubjikā, Vakrakubjikā, Aghorakubjikā and Chaturanvaya-śāmbhava.
उपमार्गे महापूर्वा काली लक्ष्मी सरस्वती |
चामुण्डा च महाविद्येश्वराख्यं शाम्भवं हृदि ||
The deities of Upāmnāya meditated upon in Anāhata Chakra are: Mahākālī, Mahālakṣmī, Mahāsarasvatī and Mahāvidyeśvara mithuna.
उत्तरे सिद्धिलक्ष्मीश्च महासिद्धिकारालिका |
कामकला गुह्यकाली हंसशाम्भव कण्ठजम् ||
The deities of Uttarāmnāya meditated upon in Viśuddi Chakra are: Siddhilakṣmī, Mahāsiddhikarālī (which is a code name for a specific form of Guhyakālī), Kāmakalā Guhyakālī (not to be confused with aṣṭādaśākṣarī) and Haṃseśvara mithuna. There is a less popular version that involves Hiraṇyakaśipūpāsitā Guhyakālī which is rarely practiced on account of it being a Krodhavidyā or Pralayavidyā.
ऊर्ध्वे बाला पञ्चदशी षोडशी परशाम्भवम् |
आज्ञा चक्र स्थितं दिव्यं श्रीविद्या क्रमसंयुतम् ||
The deities of ūrdhvāmnāya meditated upon in ājñā Chakra are: Bālā, Shuddha Pañcadaśī, ṣoḍaśī and Pareśvara śāmbhava kūṭa.