diff --git a/Eigen/src/SVD/BDCSVD.h b/Eigen/src/SVD/BDCSVD.h
index b786de9bb..9af96ec31 100644
--- a/Eigen/src/SVD/BDCSVD.h
+++ b/Eigen/src/SVD/BDCSVD.h
@@ -163,7 +163,7 @@ public:
    */
   EIGEN_DEPRECATED
   BDCSVD(Index rows, Index cols, unsigned int computationOptions) : m_algoswap(16), m_numIters(0) {
-    internal::check_svd_options_assertions<MatrixType, Options>(computationOptions);
+    internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, rows, cols);
     allocate(rows, cols, computationOptions);
   }
 
@@ -190,7 +190,7 @@ public:
    */
   EIGEN_DEPRECATED
   BDCSVD(const MatrixType& matrix, unsigned int computationOptions) : m_algoswap(16), m_numIters(0) {
-    internal::check_svd_options_assertions<MatrixType, Options>(computationOptions);
+    internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, matrix.rows(), matrix.cols());
     compute_impl(matrix, computationOptions);
   }
 
@@ -214,7 +214,7 @@ public:
    */
   EIGEN_DEPRECATED
   BDCSVD& compute(const MatrixType& matrix, unsigned int computationOptions) {
-    internal::check_svd_options_assertions<MatrixType, Options>(computationOptions);
+    internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, matrix.rows(), matrix.cols());
     return compute_impl(matrix, computationOptions);
   }
 
diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h
index 16ae8045c..8ae583a8e 100644
--- a/Eigen/src/SVD/JacobiSVD.h
+++ b/Eigen/src/SVD/JacobiSVD.h
@@ -568,7 +568,7 @@ class JacobiSVD : public SVDBase<JacobiSVD<MatrixType_, Options> > {
    */
   EIGEN_DEPRECATED
   JacobiSVD(Index rows, Index cols, unsigned int computationOptions) {
-    internal::check_svd_options_assertions<MatrixType, Options>(computationOptions);
+    internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, rows, cols);
     allocate(rows, cols, computationOptions);
   }
 
@@ -593,7 +593,7 @@ class JacobiSVD : public SVDBase<JacobiSVD<MatrixType_, Options> > {
    */
   EIGEN_DEPRECATED
   JacobiSVD(const MatrixType& matrix, unsigned int computationOptions) {
-    internal::check_svd_options_assertions<MatrixType, Options>(computationOptions);
+    internal::check_svd_options_assertions<MatrixType, Options>(computationOptions, matrix.rows(), matrix.cols());
     compute_impl(matrix, computationOptions);
   }
 
@@ -615,7 +615,7 @@ class JacobiSVD : public SVDBase<JacobiSVD<MatrixType_, Options> > {
    */
   EIGEN_DEPRECATED
   JacobiSVD& compute(const MatrixType& matrix, unsigned int computationOptions) {
-    internal::check_svd_options_assertions<MatrixType, Options>(m_computationOptions);
+    internal::check_svd_options_assertions<MatrixType, Options>(m_computationOptions, matrix.rows(), matrix.cols());
     return compute_impl(matrix, computationOptions);
   }
 
diff --git a/Eigen/src/SVD/SVDBase.h b/Eigen/src/SVD/SVDBase.h
index e4ef257f8..85b3e2057 100644
--- a/Eigen/src/SVD/SVDBase.h
+++ b/Eigen/src/SVD/SVDBase.h
@@ -37,18 +37,19 @@ constexpr int should_svd_compute_full_u(int options) { return options & ComputeF
 constexpr int should_svd_compute_thin_v(int options) { return options & ComputeThinV; }
 constexpr int should_svd_compute_full_v(int options) { return options & ComputeFullV; }
 
-template <typename MatrixType, int Options>
-void check_svd_options_assertions(unsigned int computationOptions) {
+template<typename MatrixType, int Options>
+void check_svd_options_assertions(unsigned int computationOptions, Index rows, Index cols) {
   EIGEN_STATIC_ASSERT((Options & ComputationOptionsBits) == 0,
                       "SVDBase: Cannot request U or V using both static and runtime options, even if they match. "
                       "Requesting unitaries at runtime is DEPRECATED: "
                       "Prefer requesting unitaries statically, using the Options template parameter.");
-  eigen_assert(
-      !(should_svd_compute_thin_u(computationOptions) && MatrixType::ColsAtCompileTime != Dynamic) &&
-      !(should_svd_compute_thin_v(computationOptions) && MatrixType::ColsAtCompileTime != Dynamic) &&
-      "SVDBase: If U or V are requested at runtime, then thin U and V are only available when "
-      "your matrix has a dynamic number of columns.");
+  eigen_assert(!(should_svd_compute_thin_u(computationOptions) && cols < rows && MatrixType::RowsAtCompileTime != Dynamic) &&
+               !(should_svd_compute_thin_v(computationOptions) && rows < cols && MatrixType::ColsAtCompileTime != Dynamic) &&
+               "SVDBase: If thin U is requested at runtime, your matrix must have more rows than columns or a dynamic number of rows."
+               "Similarly, if thin V is requested at runtime, you matrix must have more columns than rows or a dynamic number of columns.");
   (void)computationOptions;
+  (void)rows;
+  (void)cols;
 }
 
 template<typename Derived> struct traits<SVDBase<Derived> >
diff --git a/test/svd_common.h b/test/svd_common.h
index 1514f674f..c6f653ab8 100644
--- a/test/svd_common.h
+++ b/test/svd_common.h
@@ -482,9 +482,9 @@ void svd_compute_checks(const MatrixType& m) {
 
 template <typename SvdType, typename MatrixType>
 void svd_check_constructor_options(const MatrixType& m, unsigned int computationOptions) {
-  const bool thinUnitary = (computationOptions & ComputeThinU) != 0 || (computationOptions & ComputeThinV) != 0;
-
-  if (SvdType::ColsAtCompileTime != Dynamic && thinUnitary) {
+  const bool fixedRowAndThinU = SvdType::RowsAtCompileTime != Dynamic && (computationOptions & ComputeThinU) != 0 && m.cols() < m.rows();
+  const bool fixedColAndThinV = SvdType::ColsAtCompileTime != Dynamic && (computationOptions & ComputeThinV) != 0 && m.rows() < m.cols();
+  if (fixedRowAndThinU || fixedColAndThinV) {
     VERIFY_RAISES_ASSERT(SvdType svd(m, computationOptions));
     return;
   }