diff --git a/src/bignum/bignum.cc b/src/bignum/bignum.cc
index cadc170..3fce460 100644
--- a/src/bignum/bignum.cc
+++ b/src/bignum/bignum.cc
@@ -363,7 +363,11 @@ bool BigNum::less_than(BigNum const& rhs) const {
         return sign_ < rhs.sign_;
     }
 
-    return do_less_than(digits_, rhs.digits_);
+    if (is_positive()) {
+        return do_less_than(digits_, rhs.digits_);
+    } else {
+        return do_less_than(rhs.digits_, digits_);
+    }
 }
 
 void BigNum::canonicalize() {
@@ -381,15 +385,15 @@ bool BigNum::is_canonicalized() const {
         return sign_ == 0;
     }
 
-    auto const leading_zeros = std::find_if(digits_.rbegin(), digits_.rend(),
-                                            [](auto v) { return v != 0; });
-    if (leading_zeros != digits_.rbegin()) {
+    // `back` is valid since there is at least one element
+    auto const has_leading_zero = digits_.back() == 0;
+    if (has_leading_zero) {
         return false;
     }
 
-    auto const overflow = std::find_if(digits_.begin(), digits_.end(),
-                                       [](auto v) { return v >= BASE; });
-    if (overflow != digits_.end()) {
+    auto const has_overflow = std::any_of(digits_.begin(), digits_.end(),
+                                          [](auto v) { return v >= BASE; });
+    if (has_overflow) {
         return false;
     }
 
diff --git a/tests/unit/bignum.cc b/tests/unit/bignum.cc
index b7306f4..1126a17 100644
--- a/tests/unit/bignum.cc
+++ b/tests/unit/bignum.cc
@@ -68,6 +68,34 @@ TEST(BigNum, comparisons_digits) {
     EXPECT_GT(ten, nine);
 }
 
+TEST(BigNum, comparisons_negative) {
+    auto const zero = BigNum(0);
+    auto const minus_one = BigNum(-1);
+    auto const minus_two = BigNum(-2);
+
+    EXPECT_LT(minus_one, zero);
+    EXPECT_LE(minus_one, zero);
+    EXPECT_LT(minus_two, minus_one);
+    EXPECT_LE(minus_two, minus_one);
+    EXPECT_LE(minus_one, minus_one);
+    EXPECT_GE(minus_two, minus_two);
+
+    EXPECT_GT(zero, minus_one);
+    EXPECT_GE(zero, minus_one);
+    EXPECT_GT(minus_one, minus_two);
+    EXPECT_GE(minus_one, minus_two);
+    EXPECT_GE(minus_one, minus_one);
+    EXPECT_GE(minus_two, minus_two);
+}
+
+TEST(BigNum, comparisons_digits_negative) {
+    auto const minus_nine = BigNum(-9);
+    auto const minus_ten = BigNum(-10);
+
+    EXPECT_LT(minus_ten, minus_nine);
+    EXPECT_GT(minus_nine, minus_ten);
+}
+
 TEST(BigNum, unary) {
     auto const zero = BigNum(0);
     auto const one = BigNum(1);