diff --git a/fuzz/Cargo.toml b/fuzz/Cargo.toml
index 5245cbe..4408af6 100644
--- a/fuzz/Cargo.toml
+++ b/fuzz/Cargo.toml
@@ -21,4 +21,8 @@ members = ["."]
 
 [[bin]]
 name = "decaf"
-path = "fuzzers/decaf.rs"
+path = "fuzz_targets/decaf.rs"
+
+[[bin]]
+name = "scalar_constructor_accepts_256bit_values"
+path = "fuzz_targets/scalar_constructor_accepts_256bit_values.rs"
diff --git a/fuzz/fuzzers/decaf.rs b/fuzz/fuzz_targets/decaf.rs
similarity index 100%
rename from fuzz/fuzzers/decaf.rs
rename to fuzz/fuzz_targets/decaf.rs
diff --git a/fuzz/fuzz_targets/scalar_constructor_accepts_256bit_values.rs b/fuzz/fuzz_targets/scalar_constructor_accepts_256bit_values.rs
new file mode 100644
index 0000000..38bba88
--- /dev/null
+++ b/fuzz/fuzz_targets/scalar_constructor_accepts_256bit_values.rs
@@ -0,0 +1,36 @@
+#![no_main]
+#[macro_use] extern crate libfuzzer_sys;
+extern crate curve25519_dalek;
+
+use curve25519_dalek::scalar::Scalar;
+
+/// Check that the Scalar constructor accepts 256-bit input values and
+/// behaves correctly on them.
+///
+/// Specifically, we take 256-bit values `a` and `b` from the fuzzer
+/// input data and check that `(a mod l) * (b mod l) == (a * b) mod l`.
+fuzz_target!(|data: &[u8]| {
+    if data.len() != 64 {
+        return;
+    }
+    let mut a_bytes = [0u8; 32];
+    let mut b_bytes = [0u8; 32];
+
+    // Set a, b to be random 256-bit integers
+    a_bytes.copy_from_slice(&data[ 0..32]);
+    b_bytes.copy_from_slice(&data[32..64]);
+
+    // Compute c = a*b (mod l)
+    let c1 = &Scalar(a_bytes) * &Scalar(b_bytes);
+
+    // Compute c = (a mod l) * (b mod l)
+    let mut tmp = [0u8; 64];
+    tmp[0..32].copy_from_slice(&a_bytes[..]);
+    let a_mod_l = Scalar::reduce(&tmp);
+    tmp[0..32].copy_from_slice(&b_bytes[..]);
+    let b_mod_l = Scalar::reduce(&tmp);
+
+    let c2 = &a_mod_l * &b_mod_l;
+
+    assert_eq!(c1, c2);
+});