diff --git a/ciborium-ll/src/hdr.rs b/ciborium-ll/src/hdr.rs
index dec1788..adfb1e9 100644
--- a/ciborium-ll/src/hdr.rs
+++ b/ciborium-ll/src/hdr.rs
@@ -107,7 +107,9 @@ impl TryFrom<Title> for Header {
 
             Title(Major::Other, Minor::More) => Self::Break,
             Title(Major::Other, Minor::This(x)) => Self::Simple(x),
-            Title(Major::Other, Minor::Next1(x)) => Self::Simple(x[0]),
+            // Two-byte sequences for simple values below 32 are not considered well-formed
+            Title(Major::Other, Minor::Next1([0..=31])) => Err(InvalidError(()))?,
+            Title(Major::Other, Minor::Next1([x])) => Self::Simple(x),
             Title(Major::Other, Minor::Next2(x)) => Self::Float(f16::from_be_bytes(x).into()),
             Title(Major::Other, Minor::Next4(x)) => Self::Float(f32::from_be_bytes(x).into()),
             Title(Major::Other, Minor::Next8(x)) => Self::Float(f64::from_be_bytes(x)),
@@ -140,6 +142,11 @@ impl From<Header> for Title {
 
             Header::Simple(x) => match x {
                 x @ 0..=23 => Title(Major::Other, Minor::This(x)),
+                // Simple(24) is irrepresentable
+                // Simple(25) to Simple(27) are floats
+                // Simple(28) to Simple(30) are reserved
+                // Should this panic or error (i.e. use TryFrom instead of From) ?
+                // See: https://www.rfc-editor.org/rfc/rfc8949.html#section-3.3
                 x => Title(Major::Other, Minor::Next1([x])),
             },
 
diff --git a/ciborium-ll/src/lib.rs b/ciborium-ll/src/lib.rs
index 5b47ba9..ecf76a4 100644
--- a/ciborium-ll/src/lib.rs
+++ b/ciborium-ll/src/lib.rs
@@ -273,12 +273,19 @@ mod tests {
             (Header::Float(INFINITY), "fb7ff0000000000000", false),
             (Header::Float(NAN), "fb7ff8000000000000", false),
             (Header::Float(-INFINITY), "fbfff0000000000000", false),
+            (Header::Simple(0), "e0", true),
+            (Header::Simple(1), "e1", true),
+            (Header::Simple(16), "f0", true),
+            (Header::Simple(17), "f1", true),
+            (Header::Simple(18), "f2", true),
+            (Header::Simple(19), "f3", true),
             (Header::Simple(simple::FALSE), "f4", true),
             (Header::Simple(simple::TRUE), "f5", true),
             (Header::Simple(simple::NULL), "f6", true),
             (Header::Simple(simple::UNDEFINED), "f7", true),
-            (Header::Simple(16), "f0", true),
-            (Header::Simple(24), "f818", true),
+            (Header::Break, "ff", true),
+            (Header::Simple(32), "f820", true),
+            (Header::Simple(64), "f840", true),
             (Header::Simple(255), "f8ff", true),
             (Header::Tag(0), "c0", true),
             (Header::Tag(1), "c1", true),
diff --git a/ciborium/tests/error.rs b/ciborium/tests/error.rs
index 2bc42d9..9619222 100644
--- a/ciborium/tests/error.rs
+++ b/ciborium/tests/error.rs
@@ -115,10 +115,10 @@ fn eof() -> Error<std::io::Error> {
     case("fe", Error::Syntax(0)),
 
     // Reserved two-byte encodings of simple values:
-    case("f800", Error::Semantic(None, "invalid type: simple, expected known simple value".into())),
-    case("f801", Error::Semantic(None, "invalid type: simple, expected known simple value".into())),
-    case("f818", Error::Semantic(None, "invalid type: simple, expected known simple value".into())),
-    case("f81f", Error::Semantic(None, "invalid type: simple, expected known simple value".into())),
+    case("f800", Error::Syntax(0)),
+    case("f801", Error::Syntax(0)),
+    case("f818", Error::Syntax(0)),
+    case("f81f", Error::Syntax(0)),
 
     // Indefinite-length string chunks not of the correct type:
     case("5f00ff", Error::Syntax(1)),