diff --git a/doc/changelog.dox b/doc/changelog.dox
index 972dec8c3..8d00867c8 100644
--- a/doc/changelog.dox
+++ b/doc/changelog.dox
@@ -224,10 +224,13 @@ See also:
 -   All batch functions in @ref Magnum/Math/FunctionsBatch.h now accept
     @ref Corrade::Containers::StridedArrayView instead of a dense array view to
     make them usable in more contexts
--   Batch @ref Math::min(Containers::StridedArrayView1D<const T>),
+-   @ref Math::Vector::min(), @ref Math::Vector::max(),
+    @ref Math::Vector::minmax() and batch
+    @ref Math::min(Containers::StridedArrayView1D<const T>),
     @ref Math::max(Containers::StridedArrayView1D<const T>) and
     @ref Math::minmax(Containers::StridedArrayView1D<const T>) functions now
-    ignore NaNs in the data, if possible. Use the batch
+    ignore NaNs in the data, if possible. Use
+    @ref Math::isNan(const Vector<size, T>&) or the batch
     @ref Math::isNan(Containers::StridedArrayView1D<const T>) to detect
     presence of NaN values if needed.
 -   Changed the way @ref Math::operator<<(Corrade::Utility::Debug&, const BoolVector<size>&)
diff --git a/src/Magnum/Math/Functions.h b/src/Magnum/Math/Functions.h
index 24de6763e..67640fd11 100644
--- a/src/Magnum/Math/Functions.h
+++ b/src/Magnum/Math/Functions.h
@@ -182,9 +182,8 @@ Equivalent to @cpp value != value @ce.
 @see @ref isInf(), @ref Constants::nan(),
     @ref isNan(Corrade::Containers::StridedArrayView1D<const T>)
 */
-template<class T> inline typename std::enable_if<IsScalar<T>::value, bool>::type isNan(T value) {
-    return std::isnan(UnderlyingTypeOf<T>(value));
-}
+/* defined in Vector.h */
+template<class T> typename std::enable_if<IsScalar<T>::value, bool>::type isNan(T value);
 
 /** @overload */
 template<std::size_t size, class T> inline BoolVector<size> isNan(const Vector<size, T>& value) {
diff --git a/src/Magnum/Math/Test/VectorTest.cpp b/src/Magnum/Math/Test/VectorTest.cpp
index 76a626d36..23798b812 100644
--- a/src/Magnum/Math/Test/VectorTest.cpp
+++ b/src/Magnum/Math/Test/VectorTest.cpp
@@ -97,6 +97,8 @@ struct VectorTest: Corrade::TestSuite::Tester {
     void max();
     void minmax();
 
+    void nanIgnoring();
+
     void projected();
     void projectedOntoNormalized();
     void projectedOntoNormalizedNotNormalized();
@@ -113,6 +115,7 @@ struct VectorTest: Corrade::TestSuite::Tester {
     void debug();
 };
 
+typedef Math::Constants<Float> Constants;
 typedef Math::Rad<Float> Rad;
 typedef Vector<2, Float> Vector2;
 typedef Vector<3, Float> Vector3;
@@ -162,6 +165,8 @@ VectorTest::VectorTest() {
               &VectorTest::max,
               &VectorTest::minmax,
 
+              &VectorTest::nanIgnoring,
+
               &VectorTest::projected,
               &VectorTest::projectedOntoNormalized,
               &VectorTest::projectedOntoNormalizedNotNormalized,
@@ -483,6 +488,26 @@ void VectorTest::minmax() {
     CORRADE_COMPARE((Vector3{-3.0f, -1.0f, 2.0f}.minmax()), expected);
 }
 
+void VectorTest::nanIgnoring() {
+    Vector3 oneNan{1.0f, Constants::nan(), -3.0f};
+    Vector3 firstNan{Constants::nan(), 1.0f, -3.0f};
+    Vector3 allNan{Constants::nan(), Constants::nan(), Constants::nan()};
+
+    CORRADE_COMPARE(oneNan.min(), -3.0f);
+    CORRADE_COMPARE(firstNan.min(), -3.0f);
+    CORRADE_COMPARE(allNan.min(), Constants::nan());
+
+    CORRADE_COMPARE(oneNan.max(), 1.0f);
+    CORRADE_COMPARE(firstNan.max(), 1.0f);
+    CORRADE_COMPARE(allNan.max(), Constants::nan());
+
+    CORRADE_COMPARE(oneNan.minmax(), std::make_pair(-3.0f, 1.0f));
+    CORRADE_COMPARE(firstNan.minmax(), std::make_pair(-3.0f, 1.0f));
+    /* Need to compare this way because of NaNs */
+    CORRADE_COMPARE(allNan.minmax().first, Constants::nan());
+    CORRADE_COMPARE(allNan.minmax().second, Constants::nan());
+}
+
 void VectorTest::projected() {
     Vector3 line(1.0f, -1.0f, 0.5f);
     Vector3 projected = Vector3(1.0f, 2.0f, 3.0f).projected(line);
diff --git a/src/Magnum/Math/Vector.h b/src/Magnum/Math/Vector.h
index c882424f9..1b303ddd8 100644
--- a/src/Magnum/Math/Vector.h
+++ b/src/Magnum/Math/Vector.h
@@ -45,6 +45,10 @@ namespace Magnum { namespace Math {
 
 #ifndef DOXYGEN_GENERATING_OUTPUT
 /* Documented in Functions.h, defined here because Vector needs them */
+template<class T> inline typename std::enable_if<IsScalar<T>::value, bool>::type isNan(T value) {
+    return std::isnan(UnderlyingTypeOf<T>(value));
+}
+
 template<class T> constexpr typename std::enable_if<IsScalar<T>::value, T>::type min(T a, T b) {
     return b < a ? b : a;
 }
@@ -599,21 +603,24 @@ template<std::size_t size, class T> class Vector {
         /**
          * @brief Minimal value in the vector
          *
-         * @see @ref Math::min(), @ref minmax()
+         * <em>NaN</em>s are ignored, unless the vector is all <em>NaN</em>s.
+         * @see @ref Math::min(), @ref minmax(), @ref Math::isNan()
          */
         T min() const;
 
         /**
          * @brief Maximal value in the vector
          *
-         * @see @ref Math::max(), @ref minmax()
+         * <em>NaN</em>s are ignored, unless the vector is all <em>NaN</em>s.
+         * @see @ref Math::max(), @ref minmax(), @ref Math::isNan()
          */
         T max() const;
 
         /**
          * @brief Minimal and maximal value in the vector
          *
-         * @see @ref min(), @ref max(), @ref Math::minmax()
+         * <em>NaN</em>s are ignored, unless the vector is all <em>NaN</em>s.
+         * @see @ref min(), @ref max(), @ref Math::minmax(), @ref Math::isNan()
          */
         std::pair<T, T> minmax() const;
 
@@ -1409,28 +1416,47 @@ template<std::size_t size, class T> inline T Vector<size, T>::product() const {
     return out;
 }
 
+namespace Implementation {
+    /* Non-floating-point types, the first is a non-NaN for sure */
+    template<std::size_t size, class T> constexpr std::size_t firstNonNan(const T(&)[size], std::false_type) {
+        return 0;
+    }
+    /* Floating-point types, return the first that's not NaN */
+    template<std::size_t size, class T> inline std::size_t firstNonNan(const T(&data)[size], std::true_type) {
+        /* Find the first non-NaN value to compare against. If all are NaN,
+           return the last value so the following loop in min/max/minmax()
+           doesn't even execute. */
+        for(std::size_t i = 0; i != size; ++i)
+            if(!isNan(data[i])) return i;
+        return size - 1;
+    }
+}
+
 template<std::size_t size, class T> inline T Vector<size, T>::min() const {
-    T out(_data[0]);
+    std::size_t i = Implementation::firstNonNan(_data, IsFloatingPoint<T>{});
+    T out(_data[i]);
 
-    for(std::size_t i = 1; i != size; ++i)
+    for(++i; i != size; ++i)
         out = Math::min(out, _data[i]);
 
     return out;
 }
 
 template<std::size_t size, class T> inline T Vector<size, T>::max() const {
-    T out(_data[0]);
+    std::size_t i = Implementation::firstNonNan(_data, IsFloatingPoint<T>{});
+    T out(_data[i]);
 
-    for(std::size_t i = 1; i != size; ++i)
+    for(++i; i != size; ++i)
         out = Math::max(out, _data[i]);
 
     return out;
 }
 
 template<std::size_t size, class T> inline std::pair<T, T> Vector<size, T>::minmax() const {
-    T min{_data[0]}, max{_data[0]};
+    std::size_t i = Implementation::firstNonNan(_data, IsFloatingPoint<T>{});
+    T min{_data[i]}, max{_data[i]};
 
-    for(std::size_t i = 1; i != size; ++i) {
+    for(++i; i != size; ++i) {
         if(_data[i] < min)
             min = _data[i];
         else if(_data[i] > max)