diff --git a/git-bisect.sh b/git-bisect.sh
index 57168b0ae4..4bcbaceb8b 100755
--- a/git-bisect.sh
+++ b/git-bisect.sh
@@ -63,40 +63,40 @@ bisect_autostart() {
 
 bisect_start() {
 	#
-	# Verify HEAD. If we were bisecting before this, reset to the
-	# top-of-line master first!
+	# Verify HEAD.
 	#
 	head=$(GIT_DIR="$GIT_DIR" git symbolic-ref -q HEAD) ||
 	head=$(GIT_DIR="$GIT_DIR" git rev-parse --verify HEAD) ||
 	die "Bad HEAD - I need a HEAD"
-	#
-	# Check that we either already have BISECT_START, or that the
-	# branches bisect, new-bisect don't exist, to not override them.
-	#
-	test -s "$GIT_DIR/BISECT_START" ||
-		if git show-ref --verify -q refs/heads/bisect ||
-		    git show-ref --verify -q refs/heads/new-bisect; then
-			die 'The branches "bisect" and "new-bisect" must not exist.'
-		fi
-	start_head=''
-	case "$head" in
-	refs/heads/bisect)
-		start_head=$(cat "$GIT_DIR/BISECT_START")
-		git checkout "$start_head" || exit
-		;;
-	refs/heads/*|$_x40)
-		# This error message should only be triggered by cogito usage,
-		# and cogito users should understand it relates to cg-seek.
-		[ -s "$GIT_DIR/head-name" ] && die "won't bisect on seeked tree"
-		start_head="${head#refs/heads/}"
-		;;
-	*)
-		die "Bad HEAD - strange symbolic ref"
-		;;
-	esac
 
 	#
-	# Get rid of any old bisect state
+	# Check if we are bisecting.
+	#
+	start_head=''
+	if test -s "$GIT_DIR/BISECT_START"
+	then
+		# Reset to the rev from where we started.
+		start_head=$(cat "$GIT_DIR/BISECT_START")
+		git checkout "$start_head" || exit
+	else
+		# Get rev from where we start.
+		case "$head" in
+		refs/heads/*|$_x40)
+			# This error message should only be triggered by
+			# cogito usage, and cogito users should understand
+			# it relates to cg-seek.
+			[ -s "$GIT_DIR/head-name" ] &&
+				die "won't bisect on seeked tree"
+			start_head="${head#refs/heads/}"
+			;;
+		*)
+			die "Bad HEAD - strange symbolic ref"
+			;;
+		esac
+	fi
+
+	#
+	# Get rid of any old bisect state.
 	#
 	bisect_clean_state
 
@@ -118,7 +118,7 @@ bisect_start() {
 		break
 		;;
 	    *)
-		rev=$(git rev-parse --verify "$arg^{commit}" 2>/dev/null) || {
+		rev=$(git rev-parse -q --verify "$arg^{commit}") || {
 		    test $has_double_dash -eq 1 &&
 		        die "'$arg' does not appear to be a valid revision"
 		    break
@@ -366,9 +366,7 @@ bisect_next() {
 	exit_if_skipped_commits "$bisect_rev"
 
 	echo "Bisecting: $bisect_nr revisions left to test after this"
-	git branch -D new-bisect 2> /dev/null
-	git checkout -q -b new-bisect "$bisect_rev" || exit
-	git branch -M new-bisect bisect
+	git checkout -q "$bisect_rev" || exit
 	git show-branch "$bisect_rev"
 }
 
@@ -415,7 +413,7 @@ bisect_reset() {
 
 bisect_clean_state() {
 	# There may be some refs packed during bisection.
-	git for-each-ref --format='%(refname) %(objectname)' refs/bisect/\* refs/heads/bisect |
+	git for-each-ref --format='%(refname) %(objectname)' refs/bisect/\* |
 	while read ref hash
 	do
 		git update-ref -d $ref $hash
diff --git a/t/t6030-bisect-porcelain.sh b/t/t6030-bisect-porcelain.sh
index c4f074d738..0626544823 100755
--- a/t/t6030-bisect-porcelain.sh
+++ b/t/t6030-bisect-porcelain.sh
@@ -322,25 +322,6 @@ test_expect_success 'bisect starting with a detached HEAD' '
 	test $HEAD = $(cat .git/BISECT_START) &&
 	git bisect reset &&
 	test $HEAD = $(git rev-parse --verify HEAD)
-
-'
-
-test_expect_success 'bisect refuses to start if branch bisect exists' '
-	git bisect reset &&
-	git branch bisect &&
-	test_must_fail git bisect start &&
-	git branch -d bisect &&
-	git checkout -b bisect &&
-	test_must_fail git bisect start &&
-	git checkout master &&
-	git branch -d bisect
-'
-
-test_expect_success 'bisect refuses to start if branch new-bisect exists' '
-	git bisect reset &&
-	git branch new-bisect &&
-	test_must_fail git bisect start &&
-	git branch -d new-bisect
 '
 
 test_expect_success 'bisect errors out if bad and good are mistaken' '
@@ -350,6 +331,25 @@ test_expect_success 'bisect errors out if bad and good are mistaken' '
 	git bisect reset
 '
 
+test_expect_success 'bisect does not create a "bisect" branch' '
+	git bisect reset &&
+	git bisect start $HASH7 $HASH1 &&
+	git branch bisect &&
+	rev_hash4=$(git rev-parse --verify HEAD) &&
+	test "$rev_hash4" = "$HASH4" &&
+	git branch -D bisect &&
+	git bisect good &&
+	git branch bisect &&
+	rev_hash6=$(git rev-parse --verify HEAD) &&
+	test "$rev_hash6" = "$HASH6" &&
+	git bisect good > my_bisect_log.txt &&
+	grep "$HASH7 is first bad commit" my_bisect_log.txt &&
+	git bisect reset &&
+	rev_hash6=$(git rev-parse --verify bisect) &&
+	test "$rev_hash6" = "$HASH6" &&
+	git branch -D bisect
+'
+
 #
 #
 test_done