diff --git a/docs/api_tools.rst b/docs/api_tools.rst
index 4add9c6..69b2a60 100644
--- a/docs/api_tools.rst
+++ b/docs/api_tools.rst
@@ -10,7 +10,7 @@ the :attr:`~gpiozero.SourceMixin.source` and
 library. These utility routines are in the ``tools`` module of GPIO Zero and
 are typically imported as follows::
 
-    from gpiozero.tools import scaled, negated, conjunction
+    from gpiozero.tools import scaled, negated, all_values
 
 Given that :attr:`~gpiozero.SourceMixin.source` and
 :attr:`~gpiozero.ValuesMixin.values` deal with infinite iterators, another
@@ -29,6 +29,8 @@ Single source conversions
 
 .. autofunction:: absoluted
 
+.. autofunction:: booleanized
+
 .. autofunction:: clamped
 
 .. autofunction:: inverted
@@ -37,8 +39,12 @@ Single source conversions
 
 .. autofunction:: post_delayed
 
+.. autofunction:: post_periodic_filtered
+
 .. autofunction:: pre_delayed
 
+.. autofunction:: pre_periodic_filtered
+
 .. autofunction:: quantized
 
 .. autofunction:: queued
@@ -56,10 +62,10 @@ Combining sources
 
 .. autofunction:: averaged
 
-.. autofunction:: summed
-
 .. autofunction:: multiplied
 
+.. autofunction:: summed
+
 Artificial sources
 ==================
 
diff --git a/gpiozero/tools.py b/gpiozero/tools.py
index 4268cea..c3611f2 100644
--- a/gpiozero/tools.py
+++ b/gpiozero/tools.py
@@ -41,10 +41,13 @@ def negated(values):
         yield not v
 
 
-def inverted(values):
+def inverted(values, input_min=0, input_max=1):
     """
-    Returns the inversion of the supplied values (1 becomes 0, 0 becomes 1,
-    0.1 becomes 0.9, etc.). For example::
+    Returns the inversion of the supplied values (*input_min* becomes
+    *input_max*, *input_max* becomes *input_min*, `input_min + 0.1` becomes
+    `input_max - 0.1`, etc.). All items in *values* are assumed to be between
+    *input_min* and *input_max* (which default to 0 and 1 respectively), and
+    the output will be in the same range. For example::
 
         from gpiozero import MCP3008, PWMLED
         from gpiozero.tools import inverted
@@ -55,8 +58,10 @@ def inverted(values):
         led.source = inverted(pot.values)
         pause()
     """
+    if input_min >= input_max:
+        raise ValueError('input_min must be smaller than input_max')
     for v in values:
-        yield 1 - v
+        yield input_min + input_max - v
 
 
 def scaled(values, output_min, output_max, input_min=0, input_max=1):
@@ -82,6 +87,8 @@ def scaled(values, output_min, output_max, input_min=0, input_max=1):
         *input_max* (inclusive) then the function will not produce values that
         lie within *output_min* to *output_max* (inclusive).
     """
+    if input_min >= input_max:
+        raise ValueError('input_min must be smaller than input_max')
     input_size = input_max - input_min
     output_size = output_max - output_min
     for v in values:
@@ -104,6 +111,8 @@ def clamped(values, output_min=0, output_max=1):
         led.source = clamped(pot.values, 0.5, 1.0)
         pause()
     """
+    if output_min >= output_max:
+        raise ValueError('output_min must be smaller than output_max')
     for v in values:
         yield min(max(v, output_min), output_max)
 
@@ -128,11 +137,11 @@ def absoluted(values):
         yield abs(v)
 
 
-def quantized(values, steps, output_min=0, output_max=1):
+def quantized(values, steps, input_min=0, input_max=1):
     """
     Returns *values* quantized to *steps* increments. All items in *values* are
-    assumed to be between *output_min* and *output_max* (use :func:`scaled` to
-    ensure this if necessary).
+    assumed to be between *input_min* and *input_max* (which default to 0 and
+    1 respectively), and the output will be in the same range.
 
     For example, to quantize values between 0 and 1 to 5 "steps" (0.0, 0.25,
     0.5, 0.75, 1.0)::
@@ -146,9 +155,72 @@ def quantized(values, steps, output_min=0, output_max=1):
         led.source = quantized(pot.values, 4)
         pause()
     """
-    output_size = output_max - output_min
-    for v in scaled(values, 0, 1, output_min, output_max):
-        yield ((int(v * steps) / steps) * output_size) + output_min
+    if steps < 1:
+        raise ValueError("steps must be 1 or larger")
+    if input_min >= input_max:
+        raise ValueError('input_min must be smaller than input_max')
+    input_size = input_max - input_min
+    for v in scaled(values, 0, 1, input_min, input_max):
+        yield ((int(v * steps) / steps) * input_size) + input_min
+
+
+def booleanized(values, min_value, max_value, hysteresis=0):
+    """
+    Returns True for each item in *values* between *min_value* and
+    *max_value*, and False otherwise. *hysteresis* can optionally be used to
+    add `hysteresis`_ which prevents the output value rapidly flipping when
+    the input value is fluctuating near the *min_value* or *max_value*
+    thresholds. For example, to light an LED only when a potentiometer is
+    between 1/4 and 3/4 of its full range::
+
+        from gpiozero import LED, MCP3008
+        from gpiozero.tools import booleanized
+        from signal import pause
+
+        led = LED(4)
+        pot = MCP3008(channel=0)
+        led.source = booleanized(pot.values, 0.25, 0.75)
+        pause()
+
+    .. _hysteresis: https://en.wikipedia.org/wiki/Hysteresis
+    """
+    if min_value >= max_value:
+        raise ValueError('min_value must be smaller than max_value')
+    min_value = float(min_value)
+    max_value = float(max_value)
+    if hysteresis < 0:
+        raise ValueError("hysteresis must be 0 or larger")
+    else:
+        hysteresis = float(hysteresis)
+    if (max_value - min_value) <= hysteresis:
+        raise ValueError('The gap between min_value and max_value must be larger than hysteresis')
+    last_state = None
+    for v in values:
+        if v < min_value:
+            new_state = 'below'
+        elif v > max_value:
+            new_state = 'above'
+        else:
+            new_state = 'in'
+        switch = False
+        if last_state == None or not hysteresis:
+            switch = True
+        elif new_state == last_state:
+            pass
+        else: # new_state != last_state
+            if last_state == 'below' and new_state == 'in':
+                switch = v >= min_value + hysteresis
+            elif last_state == 'in' and new_state == 'below':
+                switch = v < min_value - hysteresis
+            elif last_state == 'in' and new_state == 'above':
+                switch = v > max_value + hysteresis
+            elif last_state == 'above' and new_state == 'in':
+                switch = v <= max_value - hysteresis
+            else: # above->below or below->above
+                switch = True
+        if switch:
+            last_state = new_state
+        yield last_state == 'in'
 
 
 def all_values(*values):
@@ -284,6 +356,8 @@ def queued(values, qsize):
         leds[4].source = btn.values
         pause()
     """
+    if qsize < 1:
+        raise ValueError("qsize must be 1 or larger")
     q = []
     it = iter(values)
     for i in range(qsize):
@@ -308,9 +382,11 @@ def smoothed(values, qsize, average=mean):
         from gpiozero.tools import smoothed
 
         with MCP3008(channel=0) as adc:
-            for smoothvalue in smoothed(adc.values, 5):
-                print smoothvalue
+            for value in smoothed(adc.values, 5):
+                print value
     """
+    if qsize < 1:
+        raise ValueError("qsize must be 1 or larger")
     q = []
     it = iter(values)
     for i in range(qsize):
@@ -327,6 +403,8 @@ def pre_delayed(values, delay):
     """
     Waits for *delay* seconds before returning each item from *values*.
     """
+    if delay < 0:
+        raise ValueError("delay must be 0 or larger")
     for v in values:
         sleep(delay)
         yield v
@@ -336,11 +414,78 @@ def post_delayed(values, delay):
     """
     Waits for *delay* seconds after returning each item from *values*.
     """
+    if delay < 0:
+        raise ValueError("delay must be 0 or larger")
     for v in values:
         yield v
         sleep(delay)
 
 
+def pre_periodic_filtered(values, block, repeat_after):
+    """
+    Blocks the first *block* items from *values*, repeating the block after
+    every *repeat_after* items, if *repeat_after* is non-zero. For example, to
+    discard the first 50 values read from an ADC::
+
+        from gpiozero import MCP3008
+        from gpiozero.tools import pre_periodic_filtered
+
+        with MCP3008(channel=0) as adc:
+            for value in pre_periodic_filtered(adc.values, 50, 0):
+                print value
+
+    Or to only display every even item read from an ADC::
+
+        from gpiozero import MCP3008
+        from gpiozero.tools import pre_periodic_filtered
+
+        with MCP3008(channel=0) as adc:
+            for value in pre_periodic_filtered(adc.values, 1, 1):
+                print value
+    """
+    if block < 1:
+        raise ValueError("block must be 1 or larger")
+    if repeat_after < 0:
+        raise ValueError("repeat_after must be 0 or larger")
+    it = iter(values)
+    if repeat_after == 0:
+        for _ in range(block):
+            next(it)
+        while True:
+            yield next(it)
+    else:
+        while True:
+            for _ in range(block):
+                next(it)
+            for _ in range(repeat_after):
+                yield next(it)
+
+
+def post_periodic_filtered(values, repeat_after, block):
+    """
+    After every *repeat_after* items, blocks the next *block* items from
+    *values*. Note that unlike :func:`pre_periodic_filtered`, *repeat_after*
+    can't be 0. For example, to block every tenth item read from an ADC::
+
+        from gpiozero import MCP3008
+        from gpiozero.tools import post_periodic_filtered
+
+        with MCP3008(channel=0) as adc:
+            for value in post_periodic_filtered(adc.values, 9, 1):
+                print value
+    """
+    if repeat_after < 1:
+        raise ValueError("repeat_after must be 1 or larger")
+    if block < 1:
+        raise ValueError("block must be 1 or larger")
+    it = iter(values)
+    while True:
+        for _ in range(repeat_after):
+            yield next(it)
+        for _ in range(block):
+            next(it)
+
+
 def random_values():
     """
     Provides an infinite source of random values between 0 and 1. For example,
diff --git a/tests/test_tools.py b/tests/test_tools.py
index 422dbec..adeef77 100644
--- a/tests/test_tools.py
+++ b/tests/test_tools.py
@@ -31,24 +31,108 @@ def test_negated():
     assert list(negated((True, True, False, False))) == [False, False, True, True]
 
 def test_inverted():
+    with pytest.raises(ValueError):
+        list(inverted((), 0, 0))
+    with pytest.raises(ValueError):
+        list(inverted((), 1, 1))
+    with pytest.raises(ValueError):
+        list(inverted((), 1, 0))
     assert list(inverted(())) == []
     assert list(inverted((1, 0, 0.1, 0.5))) == [0, 1, 0.9, 0.5]
+    assert list(inverted((1, 0, 0.1, 0.5), 0, 1)) == [0, 1, 0.9, 0.5]
+    assert list(inverted((-1, 0, -0.1, -0.5), -1, 0)) == [0, -1, -0.9, -0.5]
+    assert list(inverted((1, 0, 0.1, 0.5, -1, -0.1, -0.5), -1, 1)) == [-1, 0, -0.1, -0.5, 1, 0.1, 0.5]
+    assert list(inverted((2, 1, 1.1, 1.5), 1, 2)) == [1, 2, 1.9, 1.5]
 
 def test_scaled():
+    with pytest.raises(ValueError):
+        list(scaled((), 0, 1, 0, 0))
+    with pytest.raises(ValueError):
+        list(scaled((), 0, 1, 1, 1))
+    with pytest.raises(ValueError):
+        list(scaled((), 0, 1, 1, 0))
+    assert list(scaled((), 0, 1)) == []
+    # no scale
     assert list(scaled((0, 1, 0.5, 0.1), 0, 1)) == [0, 1, 0.5, 0.1]
+    assert list(scaled((0, 1, 0.5, 0.1), 0, 1, 0, 1)) == [0, 1, 0.5, 0.1]
+    # multiply by 2
+    assert list(scaled((0, 1, 0.5, 0.1), 0, 2, 0, 1)) == [0, 2, 1, 0.2]
+    # add 1
+    assert list(scaled((0, 1, 0.5, 0.1), 1, 2, 0, 1)) == [1, 2, 1.5, 1.1]
+    # multiply by 2 then add 1
+    assert list(scaled((0, 1, 0.5, 0.1), 1, 3, 0, 1)) == [1, 3, 2, 1.2]
+    # add 1 then multiply by 2
+    assert list(scaled((0, 1, 0.5, 0.1), 2, 4, 0, 1)) == [2, 4, 3, 2.2]
+    # invert
+    assert list(scaled((0, 1, 0.5, 0.1), 1, 0, 0, 1)) == [1, 0, 0.5, 0.9]
+    # multiply by -1 then subtract 1
+    assert list(scaled((0, 1, 0.5, 0.1), -1, -2, 0, 1)) == [-1, -2, -1.5, -1.1]
+    # scale 0->1 to -1->+1
     assert list(scaled((0, 1, 0.5, 0.1), -1, 1)) == [-1, 1, 0.0, -0.8]
+    assert list(scaled((0, 1, 0.5, 0.1), -1, 1, 0, 1)) == [-1, 1, 0.0, -0.8]
+    # scale -1->+1 to 0->1
+    assert list(scaled((-1, 1, 0.0, -0.5), 0, 1, -1, 1)) == [0, 1, 0.5, 0.25]
 
 def test_clamped():
-    assert list(clamped((-1, 0, 1, 2))) == [0, 0, 1, 1]
+    with pytest.raises(ValueError):
+        list(clamped((), 0, 0))
+    with pytest.raises(ValueError):
+        list(clamped((), 1, 1))
+    with pytest.raises(ValueError):
+        list(clamped((), 1, 0))
+    assert list(clamped(())) == []
+    assert list(clamped((-2, -1, -0.5, 0, 0.5, 1, 2))) == [0, 0, 0, 0, 0.5, 1, 1]
+    assert list(clamped((-2, -1, -0.5, 0, 0.5, 1, 2), 0, 1)) == [0, 0, 0, 0, 0.5, 1, 1]
+    assert list(clamped((-2, -1, -0.5, 0, 0.5, 1, 2), -1, 1)) == [-1, -1, -0.5, 0, 0.5, 1, 1]
+    assert list(clamped((-2, -1, -0.5, 0, 0.5, 1, 2), -2, 2)) == [-2, -1, -0.5, 0, 0.5, 1, 2]
 
 def test_absoluted():
+    assert list(absoluted(())) == []
     assert list(absoluted((-2, -1, 0, 1, 2))) == [2, 1, 0, 1, 2]
 
 def test_quantized():
+    with pytest.raises(ValueError):
+        list(quantized((), 0))
+    with pytest.raises(ValueError):
+        list(quantized((), 4, 0, 0))
+    with pytest.raises(ValueError):
+        list(quantized((), 4, 1, 1))
+    with pytest.raises(ValueError):
+        list(quantized((), 4, 1, 0))
+    assert list(quantized((), 4)) == []
     assert list(quantized((0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1), 4)) == [
             0.0, 0.0, 0.0, 0.25, 0.25, 0.5, 0.5, 0.5, 0.75, 0.75, 1.0]
+    assert list(quantized((0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1), 4, 0, 1)) == [
+            0.0, 0.0, 0.0, 0.25, 0.25, 0.5, 0.5, 0.5, 0.75, 0.75, 1.0]
     assert list(quantized((0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1), 5)) == [
             0.0, 0.0, 0.2, 0.2, 0.4, 0.4, 0.6, 0.6, 0.8, 0.8, 1.0]
+    assert list(quantized((0, 0.25, 0.5, 0.75, 1.0, 1.5, 1.75, 2.0), 2, 0, 2)) == [
+            0.0, 0.0, 0.0, 0.0, 1.0, 1.0, 1.0, 2.0]
+    assert list(quantized((1, 1.25, 1.5, 1.75, 2.0, 2.5, 2.75, 3.0), 2, 1, 3)) == [
+            1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0]
+
+def test_booleanized():
+    with pytest.raises(ValueError):
+        list(booleanized((), 0, 0))
+    with pytest.raises(ValueError):
+        list(booleanized((), 1, 1))
+    with pytest.raises(ValueError):
+        list(booleanized((), 1, 0))
+    with pytest.raises(ValueError):
+        list(booleanized((), 0, 0.5, -0.2))
+    with pytest.raises(ValueError):
+        list(booleanized((), 0, 0.5, 0.5))
+    assert list(booleanized((), 0, 0.5)) == []
+    assert list(booleanized((0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1), 0, 0.5)) == [
+            True, True, True, True, True, True, False, False, False, False, False]
+    assert list(booleanized((0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 0), 0.25, 0.75)) == [
+            False, False, False, True, True, True, True, True, False, False, False, False]
+    assert list(booleanized((0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1, 0), 0.25, 0.75, 0.2)) == [
+            False, False, False, False, False, True, True, True, True, True, False, False]
+    assert list(booleanized((1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0, 1), 0.25, 0.75)) == [
+            False, False, False, True, True, True, True, True, False, False, False, False]
+    assert list(booleanized((1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0, 1), 0.25, 0.75, 0.2)) == [
+            False, False, False, False, False, True, True, True, True, True, False, False]
 
 def test_all_values():
     assert list(all_values(())) == []
@@ -62,52 +146,128 @@ def test_any_values():
 
 def test_averaged():
     assert list(averaged(())) == []
+    assert list(averaged((0, 0.5, 1))) == [0, 0.5, 1]
     assert list(averaged((0, 0.5, 1), (1, 1, 1))) == [0.5, 0.75, 1]
 
 def test_summed():
     assert list(summed(())) == []
+    assert list(summed((0, 0.5, 0.5, 1))) == [0, 0.5, 0.5, 1]
     assert list(summed((0, 0.5, 0.5, 1), (1, 0.5, 1, 1))) == [1, 1, 1.5, 2]
 
 def test_multiplied():
     assert list(multiplied(())) == []
+    assert list(multiplied((0, 0.5, 0.5, 1))) == [0, 0.5, 0.5, 1]
     assert list(multiplied((0, 0.5, 0.5, 1), (1, 0.5, 1, 1))) == [0, 0.25, 0.5, 1]
 
 def test_queued():
+    with pytest.raises(ValueError):
+        list(queued((), 0))
+    assert list(queued((), 5)) == []
     assert list(queued((1, 2, 3, 4, 5), 5)) == [1]
     assert list(queued((1, 2, 3, 4, 5, 6), 5)) == [1, 2]
 
 def test_smoothed():
+    with pytest.raises(ValueError):
+        list(smoothed((), 0))
+    assert list(smoothed((), 5)) == []
     assert list(smoothed((1, 2, 3, 4, 5), 5)) == [3.0]
     assert list(smoothed((1, 2, 3, 4, 5, 6), 5)) == [3.0, 4.0]
+    assert list(smoothed((1, 2, 3, 4, 5, 6), 5, average=mean)) == [3.0, 4.0]
     assert list(smoothed((1, 1, 1, 4, 5, 5), 5, average=mean)) == [2.4, 3.2]
     assert list(smoothed((1, 1, 1, 4, 5, 5), 5, average=median)) == [1, 4]
 
 def test_pre_delayed():
+    with pytest.raises(ValueError):
+        list(pre_delayed((), -1))
+    assert list(pre_delayed((), 0.01)) == []
+    count = 0
     start = time()
     for v in pre_delayed((0, 0, 0), 0.01):
+        count += 1
         assert v == 0
         assert time() - start >= 0.01
         start = time()
+    assert count == 3
 
 def test_post_delayed():
+    with pytest.raises(ValueError):
+        list(post_delayed((), -1))
+    assert list(post_delayed((), 0.01)) == []
+    count = 0
     start = time()
     for v in post_delayed((1, 2, 2), 0.01):
+        count += 1
         if v == 1:
             assert time() - start < 0.01
-        else:
+        elif v == 2:
             assert time() - start >= 0.01
+        else:
+            assert False
         start = time()
     assert time() - start >= 0.01
+    assert count == 3
+
+def test_pre_periodic_filtered():
+    with pytest.raises(ValueError):
+        list(pre_periodic_filtered((), 2, -1))
+    with pytest.raises(ValueError):
+        list(pre_periodic_filtered((), 0, 0))
+    assert list(pre_periodic_filtered((), 2, 0)) == []
+    assert list(pre_periodic_filtered((1, 2, 3, 4, 5, 6, 7, 8, 9, 10), 2, 0)) == [3, 4, 5, 6, 7, 8, 9, 10]
+    assert list(pre_periodic_filtered((1, 2, 3, 4, 5, 6, 7, 8, 9, 10), 1, 1)) == [2, 4, 6, 8, 10]
+    assert list(pre_periodic_filtered((1, 2, 3, 4, 5, 6, 7, 8, 9, 10), 1, 2)) == [2, 3, 5, 6, 8, 9]
+    assert list(pre_periodic_filtered((1, 2, 3, 4, 5, 6, 7, 8, 9, 10), 2, 1)) == [3, 6, 9]
+
+def test_post_periodic_filtered():
+    with pytest.raises(ValueError):
+        list(post_periodic_filtered((), 1, 0))
+    with pytest.raises(ValueError):
+        list(post_periodic_filtered((), 0, 1))
+    assert list(pre_periodic_filtered((), 1, 1)) == []
+    assert list(post_periodic_filtered((1, 2, 3, 4, 5, 6, 7, 8, 9, 10), 1, 1)) == [1, 3, 5, 7, 9]
+    assert list(post_periodic_filtered((1, 2, 3, 4, 5, 6, 7, 8, 9, 10), 1, 2)) == [1, 4, 7, 10]
+    assert list(post_periodic_filtered((1, 2, 3, 4, 5, 6, 7, 8, 9, 10), 2, 1)) == [1, 2, 4, 5, 7, 8, 10]
 
 def test_random_values():
-    for i, v in zip(range(1000), random_values()):
+    for _, v in zip(range(1000), random_values()):
         assert 0 <= v <= 1
 
 def test_sin_values():
+    firstval = None
     for i, v in zip(range(1000), sin_values()):
+        assert -1 <= v <= 1
         assert isclose(v, sin(radians(i)), abs_tol=1e-9)
+        if i == 0:
+            firstval = v
+        else:
+            if i % 360 == 0:
+                assert v == firstval
+    for period in (360, 100):
+        firstval = None
+        for i, v in zip(range(1000), sin_values(period)):
+            assert -1 <= v <= 1
+            if i == 0:
+                firstval = v
+            else:
+                if i % period == 0:
+                    assert v == firstval
 
 def test_cos_values():
+    firstval = None
     for i, v in zip(range(1000), cos_values()):
+        assert -1 <= v <= 1
         assert isclose(v, cos(radians(i)), abs_tol=1e-9)
-
+        if i == 0:
+            firstval = v
+        else:
+            if i % 360 == 0:
+                assert v == firstval
+    for period in (360, 100):
+        firstval = None
+        for i, v in zip(range(1000), cos_values(period)):
+            assert -1 <= v <= 1
+            if i == 0:
+                firstval = v
+            else:
+                if i % period == 0:
+                    assert v == firstval