Rabbi Chayim Palachi (Turkey, 1788-1868), in his work "Tochechat Chayim," discusses the importance of repenting specifically during the six weeks known as "Shovevim" for sins involving immodesty and immoral conduct. The word "Shovevim" is an acronym representing the names of the first six Parashiyot of the Book of Shemot: Shemot, Vaera, Bo, Beshalach, Yitro and Mishpatim. The weeks when these Parashiyot are read are especially suited for earning atonement for immodest or illicit behavior. Therefore, although one must always exercise care to avoid these transgressions, during this period it is particularly important to repent for these sins and heighten one's awareness of these spiritual ills.
In addition, Rabbi Chayim Palachi enumerates several specific measures that one should take during these weeks to earn atonement for sins of immorality. It must be emphasized that the primary and most important element is reinforcing one's commitment to proper conduct in these areas. Nevertheless, the following practices are also recommended as effective means of atonement for sins of this nature:
1) One should make an effort to immerse in a Halachically valid Mikveh during these weeks, as this adds a dimension of holiness and purity to a person.
2) One must make a special effort to pray with concentration during these weeks, particularly during the recitation of Shema, and, even more so, during the recitation of the bedtime Shema. One should ensure – all year round, but especially during these weeks – to recite the entire text of Keri'at Shema Al Ha'mita as printed in the Siddurim. The Arizal (Rabbi Yitzchak Luria, Israel, 1534-1572) commented that the recitation of the bedtime Shema has the capacity to eliminate the 1,125 "Mazikin" (harmful spiritual forces) that threaten a person as he sleeps due to his sins.
3) It is recommended to don Rabbenu Tam Tefillin – in addition to the standard, Rashi Tefillin – during these weeks. The script in the Tefillin contains forty-two references to the Name of God, and thus by wearing Rabbenu Tam Tefillin in addition to Rashi Tefillin, one wears a total of eighty-four references to God's Name. Rabbi Chayim Palachi writes that this takes the place of the eighty-four fasts that are required to earn atonement for certain sins. Since most people are incapable of observing so many fasts, it is advisable to wear Rabbenu Tam Tefillin – particularly during the weeks of "Shovevim" – in lieu of the eighty-four fasts.
4) Especially during these weeks, one should donate coins to charity as he recites "Va'yevarech David" towards the end of the daily "Pesukei De'zimra" service. The Arizal held that one should give three coins – first two, and then one – to charity while reciting this section of "Pesukei De'zimra."
5) Reading Tehillim is especially beneficial during this period. The Chid"a (Rabbi Chayim Yosef David Azulai, 1724-1806) found an allusion to this concept in the first verse of the Book of Shemot: the final letters of the first five words of this verse ("Ve'eileh Shemot Benei Yisrael Ha'ba'im") spell the word "Tehillim," alluding to the value of reciting Tehillim during the weeks when we begin reading the Book of Shemot.
As mentioned earlier, the most important measure that should be taken during this period as a means of atonement is sincere Teshuva, which includes the study of Torah. This is an appropriate time for one to reinforce his commitment to regular Torah study, which, in addition to the measures outlined above, will hopefully earn one complete atonement for misdeeds committed in the area of immodesty and immoral conduct.