diff --git a/share/completions/git.fish b/share/completions/git.fish
index df6d045dc..5b21f7ef2 100644
--- a/share/completions/git.fish
+++ b/share/completions/git.fish
@@ -1,7 +1,7 @@
 # fish completion for git
 
 function __fish_git_branches
-  git branch --no-color -a 2>/dev/null | sed 's/^..//'
+  git branch --no-color -a 2>/dev/null | sed 's/^..//; s/^remotes\///'
 end
 
 function __fish_git_tags
@@ -93,6 +93,7 @@ complete -f -c git -n '__fish_git_needs_command'    -a checkout -d 'Checkout and
 complete -f -c git -n '__fish_git_using_command checkout'  -a '(__fish_git_branches)' --description 'Branch'
 complete -f -c git -n '__fish_git_using_command checkout'  -a '(__fish_git_tags)' --description 'Tag'
 complete -f -c git -n '__fish_git_using_command checkout' -s b -d 'Create a new branch'
+complete -f -c git -n '__fish_git_using_command checkout' -s t -l track -d 'Track a new branch'
 # TODO options
 
 ### apply
@@ -110,11 +111,14 @@ complete -f -c git -n '__fish_git_needs_command' -a bisect -d 'Find the change t
 ### branch
 complete -f -c git -n '__fish_git_needs_command' -a branch -d 'List, create, or delete branches'
 complete -f -c git -n '__fish_git_using_command branch' -a '(__fish_git_branches)' -d 'Branch'
-complete -f -c git -n '__fish_git_using_command branch' -s d -d 'Delete Branch'
+complete -f -c git -n '__fish_git_using_command branch' -s d -d 'Delete branch'
 complete -f -c git -n '__fish_git_using_command branch' -s D -d 'Force deletion of branch'
 complete -f -c git -n '__fish_git_using_command branch' -s m -d 'Rename branch'
 complete -f -c git -n '__fish_git_using_command branch' -s M -d 'Force renaming branch'
 complete -f -c git -n '__fish_git_using_command branch' -s a -d 'Lists both local and remote branches'
+complete -f -c git -n '__fish_git_using_command branch' -s t -l track -d 'Track remote branch'
+complete -f -c git -n '__fish_git_using_command branch' -l no-track -d 'Do not track remote branch'
+complete -f -c git -n '__fish_git_using_command branch' -l set-upstream -d 'Set remote branch to track'
 
 ### cherry-pick
 complete -f -c git -n '__fish_git_needs_command' -a cherry-pick -d 'Apply the change introduced by an existing commit'
@@ -243,4 +247,4 @@ complete -f -c git -n '__fish_git_using_command submodule' -a 'add status init u
 complete -f -c git -n '__fish_git_needs_command' -a whatchanged -d 'Show logs with difference each commit introduces'
 
 ## Aliases (custom user-defined commands)
-complete -c git -n '__fish_git_needs_command' -a '(git config --get-regexp alias | sed -e "s/^alias\.\(\S\+\).*/\1/")' -d 'Alias (user-defined command)'
+complete -c git -n '__fish_git_needs_command' -a '(git config --get-regexp alias | sed "s/^alias\.\([^ ]*\).*/\1/")' -d 'Alias (user-defined command)'