diff --git a/pkg/cmd/run/view/fixtures/run_log.zip b/pkg/cmd/run/view/fixtures/run_log.zip
index 60701d925..425ba09dd 100644
Binary files a/pkg/cmd/run/view/fixtures/run_log.zip and b/pkg/cmd/run/view/fixtures/run_log.zip differ
diff --git a/pkg/cmd/run/view/view.go b/pkg/cmd/run/view/view.go
index 5b8a1da87..0dafbcc09 100644
--- a/pkg/cmd/run/view/view.go
+++ b/pkg/cmd/run/view/view.go
@@ -555,15 +555,25 @@ func getJobNameForLogFilename(name string) string {
 	return sanitizedJobName
 }
 
+// A job run log file is a top-level .txt file whose name starts with an ordinal
+// number; e.g., "0_jobname.txt".
 func jobLogFilenameRegexp(job shared.Job) *regexp.Regexp {
 	sanitizedJobName := getJobNameForLogFilename(job.Name)
-	re := fmt.Sprintf(`^-?\d+_%s\.txt`, regexp.QuoteMeta(sanitizedJobName))
+	re := fmt.Sprintf(`^\d+_%s\.txt$`, regexp.QuoteMeta(sanitizedJobName))
+	return regexp.MustCompile(re)
+}
+
+// A legacy job run log file is a top-level .txt file whose name starts with a
+// negative number which is the ID of the run; e.g., "-2147483648_jobname.txt".
+func legacyJobLogFilenameRegexp(job shared.Job) *regexp.Regexp {
+	sanitizedJobName := getJobNameForLogFilename(job.Name)
+	re := fmt.Sprintf(`^-\d+_%s\.txt$`, regexp.QuoteMeta(sanitizedJobName))
 	return regexp.MustCompile(re)
 }
 
 func stepLogFilenameRegexp(job shared.Job, step shared.Step) *regexp.Regexp {
 	sanitizedJobName := getJobNameForLogFilename(job.Name)
-	re := fmt.Sprintf(`^%s\/%d_.*\.txt`, regexp.QuoteMeta(sanitizedJobName), step.Number)
+	re := fmt.Sprintf(`^%s\/%d_.*\.txt$`, regexp.QuoteMeta(sanitizedJobName), step.Number)
 	return regexp.MustCompile(re)
 }
 
@@ -662,26 +672,31 @@ func truncateAsUTF16(str string, max int) string {
 //     where the ID can apparently be negative.
 func attachRunLog(rlz *zip.Reader, jobs []shared.Job) {
 	for i, job := range jobs {
-		re := jobLogFilenameRegexp(job)
-		for _, file := range rlz.File {
-			if re.MatchString(file.Name) {
-				jobs[i].Log = file
-				break
-			}
+		// As a highest priority, we try to use the step logs first. We have seen zips that surprisingly contain
+		// step logs, normal job logs and legacy job logs. In this case, both job logs would be ignored. We have
+		// never seen a zip containing both job logs and no step logs, however, it may be possible. In that case
+		// let's prioritise the normal log over the legacy one.
+		jobLog := matchFileInZIPArchive(rlz, jobLogFilenameRegexp(job))
+		if jobLog == nil {
+			jobLog = matchFileInZIPArchive(rlz, legacyJobLogFilenameRegexp(job))
 		}
+		jobs[i].Log = jobLog
 
 		for j, step := range job.Steps {
-			re := stepLogFilenameRegexp(job, step)
-			for _, file := range rlz.File {
-				if re.MatchString(file.Name) {
-					jobs[i].Steps[j].Log = file
-					break
-				}
-			}
+			jobs[i].Steps[j].Log = matchFileInZIPArchive(rlz, stepLogFilenameRegexp(job, step))
 		}
 	}
 }
 
+func matchFileInZIPArchive(zr *zip.Reader, re *regexp.Regexp) *zip.File {
+	for _, file := range zr.File {
+		if re.MatchString(file.Name) {
+			return file
+		}
+	}
+	return nil
+}
+
 func displayRunLog(w io.Writer, jobs []shared.Job, failed bool) error {
 	for _, job := range jobs {
 		// To display a run log, we first try to compile it from individual step
diff --git a/pkg/cmd/run/view/view_test.go b/pkg/cmd/run/view/view_test.go
index 2205a9031..2d150934f 100644
--- a/pkg/cmd/run/view/view_test.go
+++ b/pkg/cmd/run/view/view_test.go
@@ -2039,8 +2039,9 @@ func TestViewRun(t *testing.T) {
 //	├── 2_cool job with no step logs.txt
 //	├── 3_sad job with no step logs.txt
 //	├── -9999999999_legacy cool job with no step logs.txt
-//	└── -9999999999_legacy sad job with no step logs.txt
-
+//	├── -9999999999_legacy sad job with no step logs.txt
+//	├── 4_cool job with both legacy and new logs.txt
+//	└── -9999999999_cool job with both legacy and new logs.txt
 func Test_attachRunLog(t *testing.T) {
 	tests := []struct {
 		name             string
@@ -2149,6 +2150,15 @@ func Test_attachRunLog(t *testing.T) {
 			wantJobFilename: "-9999999999_legacy cool job with no step logs.txt",
 			wantStepMatch:   false,
 		},
+		{
+			name: "matching job name with both normal and legacy filename",
+			job: shared.Job{
+				Name: "cool job with both legacy and new logs",
+			},
+			wantJobMatch:    true,
+			wantJobFilename: "4_cool job with both legacy and new logs.txt",
+			wantStepMatch:   false,
+		},
 		{
 			name: "one job name is a suffix of another",
 			job: shared.Job{