diff --git a/stan/math/prim/constraint/cholesky_corr_free.hpp b/stan/math/prim/constraint/cholesky_corr_free.hpp
index 334895546c4..fc2e689e554 100644
--- a/stan/math/prim/constraint/cholesky_corr_free.hpp
+++ b/stan/math/prim/constraint/cholesky_corr_free.hpp
@@ -16,10 +16,9 @@ inline auto cholesky_corr_free(const T& x) {
   using Eigen::Matrix;
   using std::sqrt;
 
-  check_square("cholesky_corr_free", "x", x);
-  // should validate lower-triangular, unit lengths
-
   const auto& x_ref = to_ref(x);
+  check_cholesky_factor_corr("cholesky_corr_free", "x", x_ref);
+
   int K = (x.rows() * (x.rows() - 1)) / 2;
   Matrix<value_type_t<T>, Dynamic, 1> z(K);
   int k = 0;
diff --git a/stan/math/prim/constraint/cov_matrix_free.hpp b/stan/math/prim/constraint/cov_matrix_free.hpp
index 4d71f179665..81b614ca162 100644
--- a/stan/math/prim/constraint/cov_matrix_free.hpp
+++ b/stan/math/prim/constraint/cov_matrix_free.hpp
@@ -38,8 +38,7 @@ template <typename T, require_eigen_t<T>* = nullptr>
 inline Eigen::Matrix<value_type_t<T>, Eigen::Dynamic, 1> cov_matrix_free(
     const T& y) {
   const auto& y_ref = to_ref(y);
-  check_square("cov_matrix_free", "y", y_ref);
-  check_nonzero_size("cov_matrix_free", "y", y_ref);
+  check_cov_matrix("cov_matrix_free", "y", y_ref);
 
   using std::log;
   int K = y_ref.rows();
diff --git a/test/unit/math/prim/constraint/cholesky_corr_transform_test.cpp b/test/unit/math/prim/constraint/cholesky_corr_transform_test.cpp
index 4f6deed1af4..5644fcb446c 100644
--- a/test/unit/math/prim/constraint/cholesky_corr_transform_test.cpp
+++ b/test/unit/math/prim/constraint/cholesky_corr_transform_test.cpp
@@ -6,8 +6,9 @@ TEST(ProbTransform, CholeskyCorrelation4) {
   using Eigen::Dynamic;
   using Eigen::Matrix;
   Matrix<double, Dynamic, Dynamic> L(4, 4);
-  L << 1, 0, 0, 0, -0.2, 0.9797959, 0, 0, 0.5, -0.3, 0.8124038, 0, 0.7, -0.2,
-      0.6, 0.3316625;
+  L << 1., 0., 0., 0., 0.137406408, 0.990514755, 0., 0., 0.182409918,
+      0.217317336, 0.958905521, 0., -0.13727584, 0.443593876, 0.837969972,
+      0.286681258;
 
   Matrix<double, Dynamic, 1> y = stan::math::cholesky_corr_free(L);
 
@@ -103,7 +104,8 @@ TEST(ProbTransform, CholeskyCorrelationRoundTrips) {
   test_cholesky_correlation_values(L2);
 
   Matrix<double, Dynamic, Dynamic> L4(4, 4);
-  L4 << 1, 0, 0, 0, -0.2, 0.9797959, 0, 0, 0.5, -0.3, 0.8124038, 0, 0.7, -0.2,
-      0.6, 0.3316625;
+  L4 << 1., 0., 0., 0., 0.14489293, 0.98944734, 0., 0., -0.050876204,
+      -0.884785168, 0.463213577, 0., -0.412684102, -0.49899983, -0.67896005,
+      0.345983023;
   test_cholesky_correlation_values(L4);
 }