Tweedle is a clean, feature-rich, free, ad-supported application. You can opt to remove the ads for $1.5.
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Pros
Pro Great theme customization
You can choose between 5 different themes, including light and dark themes. You can also manually set up Tweedle colors yourself, choose to display avatars or not and what you want actionbar to look like.
Pro Detailed notification settings
You can have separate notification settings for your timeline, mentions and direct messages for each account. Refresh time can be set between a minute and 4 hours.
Pro Customizable columns
You can customize what columns you want shown - home, mentions, messages, favorites, retweets, trends, search and lists.
Pro Embeds photo & video previews
Tweedle embeds previews of photos and videos in your timeline.
Pro Multiple user support
Allows for easy switching between different Twitter accounts within the app.
Pro SSL encryption
You can have all your communication with Twitter encrypted.
Pro Real-time notifications
You can choose to have instant push notifications when on Wi-Fi.
Pro Mute function
You can remove tweets of a user from your timeline without having to unfollow them. As well as mute specific words or hashtags.
Pro In-app browser
Allows following links without having to leave the application.