diff --git a/alignment.cabal b/alignment.cabal
--- a/alignment.cabal
+++ b/alignment.cabal
@@ -1,7 +1,7 @@
 -- documentation, see http://haskell.org/cabal/users-guide/
 
 name:                   alignment
-version:                0.1.0.1
+version:                0.1.0.2
 synopsis:               Zip-alignment
 description:
   <<https://system-f.gitlab.io/logo/systemf-450x450.jpg>>
@@ -18,7 +18,7 @@
 cabal-version:          >=1.10
 homepage:               https://gitlab.com/system-f/alignment
 bug-reports:            https://gitlab.com/system-f/alignment/issues
-tested-with:             GHC == 7.10.3, GHC == 8.0.2, GHC == 8.2.2, GHC == 8.4.3, GHC == 8.6.1
+tested-with:            GHC == 7.10.3, GHC == 8.0.2, GHC == 8.2.2, GHC == 8.4.3, GHC == 8.6.1
 
 source-repository       head
   type:                 git
diff --git a/changelog.md b/changelog.md
--- a/changelog.md
+++ b/changelog.md
@@ -1,3 +1,7 @@
+0.1.0.2
+
+* Add `allThoseAOr` and `allThoseBOr`.
+
 0.1.0.1
 
 * Add `alignWith`.
diff --git a/src/Data/Alignment.hs b/src/Data/Alignment.hs
--- a/src/Data/Alignment.hs
+++ b/src/Data/Alignment.hs
@@ -18,8 +18,10 @@
 , allThose
 , allThoseA
 , allThoseA'
+, allThoseAOr
 , allThoseB
 , allThoseB'
+, allThoseBOr
 , allTheseThoseA
 , allTheseThoseB
 ) where
@@ -47,7 +49,7 @@
 import Data.Either ( Either(..) )
 import Data.Eq ( Eq((==)) )
 import Data.Foldable ( Foldable(foldMap) )
-import Data.Functor ( Functor(fmap) )
+import Data.Functor ( Functor(fmap), (<$) )
 import Data.Functor.Apply ( Apply((<.>), liftF2) )
 import Data.Functor.Classes
     ( compare1,
@@ -65,6 +67,9 @@
 import Data.Traversable ( Traversable(traverse) )
 import GHC.Show ( Show(showsPrec) )
 
+-- $setup
+-- >>> import Prelude
+
 data This f a b =
   This
     (f (a, b))
@@ -491,6 +496,33 @@
 
 -- |
 --
+-- >>> over allThoseBOr reverse (This [("abc", 'x'), ("def", 'y')] Nothing)
+-- This [("abc",'x'),("def",'y')] Nothing
+-- >>> over allThoseBOr reverse (This [("abc", 'x'), ("def", 'y')] (Just (Left ("abc":|["def"]))))
+-- This [("abc",'x'),("def",'y')] Just (Left ("abc" :| ["def"]))
+-- >>> over allThoseBOr reverse (This [("abc", 'x'), ("def", 'y')] (Just (Right ('a':|"bcde"))))
+-- This [("abc",'x'),("def",'y')] Just (Right ('e' :| "dcba"))
+-- >>> Control.Lens.preview allThoseBOr (This [("abc", 'x'), ("def", 'y')] Nothing)
+-- Just ""
+-- >>> Control.Lens.preview allThoseBOr (This [("abc", 'x'), ("def", 'y')] (Just (Left ("abc":|["def"]))))
+-- Nothing
+-- >>> Control.Lens.preview allThoseBOr (This [("abc", 'x'), ("def", 'y')] (Just (Right ('a':|"bcde"))))
+-- Just "abcde"
+allThoseAOr ::
+  Traversal'
+    (This f a b)
+    [a]
+allThoseAOr f (This t Nothing) =
+  This t <$> (Nothing <$ f [])
+allThoseAOr _ th@(This _ (Just (Right _))) =
+  pure th
+allThoseAOr f (This t (Just (Left a))) =
+  let lst [] = Nothing
+      lst (x:y) = Just (x:|y)
+  in  This t <$> (fmap Left . lst <$> f (NonEmpty.toList a))
+
+-- |
+--
 -- >>> over allThoseB (fmap Data.Char.toUpper) (This [("abc", 'x'), ("def", 'y')] Nothing)
 -- This [("abc",'x'),("def",'y')] Nothing
 -- >>> over allThoseB (fmap Data.Char.toUpper) (This [("abc", 'x'), ("def", 'y')] (Just (Left ("abc":|["def"]))))
@@ -531,6 +563,33 @@
     b
 allThoseB' =
   allThoseB . traverse
+
+-- |
+--
+-- >>> over allThoseBOr reverse (This [("abc", 'x'), ("def", 'y')] Nothing)
+-- This [("abc",'x'),("def",'y')] Nothing
+-- >>> over allThoseBOr reverse (This [("abc", 'x'), ("def", 'y')] (Just (Left ("abc":|["def"]))))
+-- This [("abc",'x'),("def",'y')] Just (Left ("abc" :| ["def"]))
+-- >>> over allThoseBOr reverse (This [("abc", 'x'), ("def", 'y')] (Just (Right ('a':|"bcde"))))
+-- This [("abc",'x'),("def",'y')] Just (Right ('e' :| "dcba"))
+-- >>> Control.Lens.preview allThoseBOr (This [("abc", 'x'), ("def", 'y')] Nothing)
+-- Just ""
+-- >>> Control.Lens.preview allThoseBOr (This [("abc", 'x'), ("def", 'y')] (Just (Left ("abc":|["def"]))))
+-- Nothing
+-- >>> Control.Lens.preview allThoseBOr (This [("abc", 'x'), ("def", 'y')] (Just (Right ('a':|"bcde"))))
+-- Just "abcde"
+allThoseBOr ::
+  Traversal'
+    (This f a b)
+    [b]
+allThoseBOr f (This t Nothing) =
+  This t <$> (Nothing <$ f [])
+allThoseBOr f (This t (Just (Right b))) =
+  let lst [] = Nothing
+      lst (x:y) = Just (x:|y)
+  in  This t <$> (fmap Right . lst <$> f (NonEmpty.toList b))
+allThoseBOr _ th@(This _ (Just (Left _))) =
+  pure th
 
 -- |
 --