diff --git a/src/isobmff.rs b/src/isobmff.rs
index 8f927ff..75be945 100644
--- a/src/isobmff.rs
+++ b/src/isobmff.rs
@@ -442,6 +442,44 @@ mod tests {
         assert!(buf.ends_with(b"xif\0"));
     }
 
+    #[test]
+    fn unknown_before_ftyp() {
+        let data =
+            b"\0\0\0\x09XXXXx\
+              \0\0\0\x14ftypmif1\0\0\0\0mif1\
+              \0\0\0\x57meta\0\0\0\0\
+                  \0\0\0\x18iloc\x01\0\0\0\0\0\0\x01\x1e\x1d\0\x01\0\0\0\x01\
+                  \0\0\0\x22iinf\0\0\0\0\0\x01\
+                      \0\0\0\x14infe\x02\0\0\0\x1e\x1d\0\0Exif\
+                  \0\0\0\x11idat\0\0\0\x01xabcd";
+        assert!(is_heif(data));
+        let exif = get_exif_attr(&mut Cursor::new(&data[..])).unwrap();
+        assert_eq!(exif, b"abcd");
+    }
+
+    #[test]
+    fn bad_exif_data_block() {
+        let data =
+            b"\0\0\0\x14ftypmif1\0\0\0\0mif1\
+              \0\0\0\x52meta\0\0\0\0\
+                  \0\0\0\x18iloc\x01\0\0\0\0\0\0\x01\x1e\x1d\0\x01\0\0\0\x01\
+                  \0\0\0\x22iinf\0\0\0\0\0\x01\
+                      \0\0\0\x14infe\x02\0\0\0\x1e\x1d\0\0Exif\
+                  \0\0\0\x0cidat\0\0\0\x01";
+        assert_err_pat!(get_exif_attr(&mut Cursor::new(&data[..])),
+                        Error::InvalidFormat("Invalid Exif header offset"));
+
+        let data =
+            b"\0\0\0\x14ftypmif1\0\0\0\0mif1\
+              \0\0\0\x51meta\0\0\0\0\
+                  \0\0\0\x18iloc\x01\0\0\0\0\0\0\x01\x1e\x1d\0\x01\0\0\0\x01\
+                  \0\0\0\x22iinf\0\0\0\0\0\x01\
+                      \0\0\0\x14infe\x02\0\0\0\x1e\x1d\0\0Exif\
+                  \0\0\0\x0bidat\0\0\0";
+        assert_err_pat!(get_exif_attr(&mut Cursor::new(&data[..])),
+                        Error::InvalidFormat("ExifDataBlock too small"));
+    }
+
     #[test]
     fn parser_box_header() {
         // size
diff --git a/src/jpeg.rs b/src/jpeg.rs
index 01fab5f..d5fc36e 100644
--- a/src/jpeg.rs
+++ b/src/jpeg.rs
@@ -125,6 +125,12 @@ mod tests {
             assert_err_pat!(get_exif_attr(&mut Cursor::new(data)),
                             Error::InvalidFormat("Broken JPEG file"));
         }
+
+        let mut data = b"\xff\xd8\xff\xe1\x00\x08Exif\0\0".to_vec();
+        get_exif_attr(&mut Cursor::new(&data)).unwrap();
+        while let Some(_) = data.pop() {
+            get_exif_attr(&mut &data[..]).unwrap_err();
+        }
     }
 
     #[test]
diff --git a/src/tiff.rs b/src/tiff.rs
index 46ea9f6..69ab000 100644
--- a/src/tiff.rs
+++ b/src/tiff.rs
@@ -531,6 +531,17 @@ mod tests {
         assert_eq!(format!("{:^10}", In(65535)), " IFD65535 ");
     }
 
+    #[test]
+    fn truncated() {
+        let mut data =
+            b"MM\0\x2a\0\0\0\x08\
+              \0\x01\x01\0\0\x03\0\0\0\x01\0\x14\0\0\0\0\0\0".to_vec();
+        parse_exif(&data).unwrap();
+        while let Some(_) = data.pop() {
+            parse_exif(&data).unwrap_err();
+        }
+    }
+
     // Before the error is returned, the IFD is parsed multiple times
     // as the 0th, 1st, ..., and n-th IFDs.
     #[test]