diff --git a/plot-doc/plot/scribblings/params.scrbl b/plot-doc/plot/scribblings/params.scrbl
index c5293c45..9ac02ddd 100644
--- a/plot-doc/plot/scribblings/params.scrbl
+++ b/plot-doc/plot/scribblings/params.scrbl
@@ -196,6 +196,17 @@ The symbol, and its size and opacity, used in point plots.
 Used as default keyword arguments of @racket[points] and @racket[points3d].
 }
 
+@deftogether[((defparam point-x-jitter x-jitter (>=/c 0) #:value 0)
+              (defparam point-y-jitter y-jitter (>=/c 0) #:value 0)
+              (defparam point-z-jitter z-jitter (>=/c 0) #:value 0))]{
+When any of @(racket x-jitter), @(racket y-jitter), or @(racket z-jitter) are non-zero,
+ @(racket points) and @(racket points3d) will produce points randomly translated from their
+ original position along the x, y, or z axis, respectively.
+For instance, if each parameter is set to 1, then @(racket points '(0 0)) will produce a random point
+ in a square of area 1 centered at @(racket '(0 0)).
+Likewise @(racket points3d) will make a random point within a unit cube centered at @(racket '(0 0 0)).
+}
+
 @deftogether[((defparam point-color color plot-color/c #:value 0)
               (defparam point-line-width width (>=/c 0) #:value 1))]{
 The color and line width of symbols used in point plots and labeled points.
diff --git a/plot-doc/plot/scribblings/renderer2d.scrbl b/plot-doc/plot/scribblings/renderer2d.scrbl
index f28910d5..5c54b0bf 100644
--- a/plot-doc/plot/scribblings/renderer2d.scrbl
+++ b/plot-doc/plot/scribblings/renderer2d.scrbl
@@ -52,6 +52,8 @@ Not every renderer-producing function has a @(racket #:label) argument; for exam
                  [#:sym sym point-sym/c (point-sym)]
                  [#:color color plot-color/c (point-color)]
                  [#:fill-color fill-color (or/c plot-color/c 'auto) 'auto]
+                 [#:x-jitter x-jitter (>=/c 0) (point-x-jitter)]
+                 [#:y-jitter y-jitter (>=/c 0) (point-y-jitter)]
                  [#:size size (>=/c 0) (point-size)]
                  [#:line-width line-width (>=/c 0) (point-line-width)]
                  [#:alpha alpha (real-in 0 1) (point-alpha)]
@@ -76,6 +78,33 @@ Readers of the first plot could only guess that the random points were generated
 
 The @(racket #:sym) argument may be any integer, a Unicode character or string, or a symbol in @(racket known-point-symbols).
 Use an integer when you need different points but don't care exactly what they are.
+
+When @(racket x-jitter) or @(racket y-jitter) is non-zero, all points are randomly translated from their original position.
+Specifically, each point @(racket p) is moved to a random location inside a rectangle centered at @(racket p) with width at most @(racket x-jitter) and height at most @(y-jitter).
+The new points will lie within [@(racket x-min), @(racket x-max)] and [@(racket y-min), @(racket y-max)] if these bounds are non-@(racket #f).
+
+@interaction[#:eval plot-eval
+                    (plot
+                      (points (for/list ([_i (in-range 999)])
+                                (list (* 10 (random)) 0))
+                              #:alpha 0.4
+                              #:y-jitter 1
+                              #:sym 'fullcircle1
+                              #:color "blue")
+                      #:x-min -5 #:x-max 5 #:y-min -5 #:y-max 5)]
+
+Randomly moving data points is almost always a bad idea, but jittering in a controlled manner can sometimes be useful.
+For example:
+@margin-note{More examples of jittering:
+             @hyperlink["http://kieranhealy.org/blog/archives/2015/02/03/another-look-at-the-california-vaccination-data/"]{Another Look at the California Vaccination Data}
+             and
+             @hyperlink["https://pavelfatin.com/typing-with-pleasure/"]{Typing with Pleasure}}
+
+@itemlist[
+  @item{To highlight the size of a dense (or @hyperlink["https://en.wiktionary.org/wiki/overplotting"]{overplotted}) sample.}
+  @item{To see the distribution of 1-dimensional data; as a substitute for box or violin plots.}
+  @item{To anonymize spatial data, showing i.e. an office's neighborhood but hiding its address.}
+]
 }
 
 @defproc[(vector-field
diff --git a/plot-doc/plot/scribblings/renderer3d.scrbl b/plot-doc/plot/scribblings/renderer3d.scrbl
index ce561551..2762e1f9 100644
--- a/plot-doc/plot/scribblings/renderer3d.scrbl
+++ b/plot-doc/plot/scribblings/renderer3d.scrbl
@@ -28,6 +28,9 @@ See @secref["renderer2d-function-arguments"] for a detailed example.
           [#:sym sym point-sym/c (point-sym)]
           [#:color color plot-color/c (point-color)]
           [#:fill-color fill-color (or/c plot-color/c 'auto) 'auto]
+          [#:x-jitter x-jitter (>=/c 0) (point-x-jitter)]
+          [#:y-jitter y-jitter (>=/c 0) (point-y-jitter)]
+          [#:z-jitter z-jitter (>=/c 0) (point-z-jitter)]
           [#:size size (>=/c 0) (point-size)]
           [#:line-width line-width (>=/c 0) (point-line-width)]
           [#:alpha alpha (real-in 0 1) (point-alpha)]
@@ -51,6 +54,13 @@ For example, a scatter plot of points sampled uniformly from the surface of a sp
                     
                     (plot3d (points3d (map vector xs ys zs) #:sym 'dot)
                             #:altitude 25)]
+
+When @(racket x-jitter), @(racket y-jitter), or @(racket z-jitter) is non-zero,
+ each point @(racket p) is translated to a random location inside a box centered at @(racket p) with width @(racket x-jitter), height @(racket y-jitter), and depth @(racket z-jitter).
+The new points will lie within [@(racket x-min), @(racket x-max)] etc. if these bounds are non-@(racket #f).
+
+Note that adding random noise to data, via jittering or otherwise, is usually a bad idea.
+See the documentation for @(racket points) for examples where jittering may be appropriate.
 }
 
 @defproc[(vector-field3d
diff --git a/plot-lib/plot/private/common/math.rkt b/plot-lib/plot/private/common/math.rkt
index 2aa88133..199ba503 100644
--- a/plot-lib/plot/private/common/math.rkt
+++ b/plot-lib/plot/private/common/math.rkt
@@ -548,6 +548,27 @@
          [x  (if a (max x a) x)])
     x))
 
+;; Return a Real drawn randomly from the interval [(- val jitter) (+ val jitter)].
+;; If #:ivl is given, result will lie within the given interval.
+(: apply-jitter (->* [Real Nonnegative-Real] [#:ivl ivl] Real))
+(define (apply-jitter val jitter #:ivl [interval unknown-ivl])
+  (let ([offset (* (random) jitter)])
+    (if (zero? (random 2))
+        (let ([val- (- val offset)])
+          (max val- (or (ivl-min interval) val-)))
+        (let ([val+ (+ val offset)])
+          (min val+ (or (ivl-max interval) val+))))))
+
+;; Precondition: all vectors in the arguments are the same length
+(:: points-apply-jitters (->* [(Listof (Vectorof Real)) (Vectorof Nonnegative-Real)] [#:ivls (U (Vectorof ivl) #f)] Void))
+(define (points-apply-jitters vals jitters #:ivls [ivls #f])
+  (for ([v (in-list vals)])
+    (for ([i (in-range (vector-length jitters))])
+      (let ([v_i (vector-ref v i)]
+            [iv  (if ivls (vector-ref ivls i) unknown-ivl)]
+            [jt  (vector-ref jitters i)])
+        (vector-set! v i (apply-jitter v_i jt #:ivl iv))))))
+
 ;; ===================================================================================================
 ;; Rectangles
 
diff --git a/plot-lib/plot/private/common/parameters.rkt b/plot-lib/plot/private/common/parameters.rkt
index fbad2b5f..7b5e3bc9 100644
--- a/plot-lib/plot/private/common/parameters.rkt
+++ b/plot-lib/plot/private/common/parameters.rkt
@@ -179,6 +179,9 @@
 
 (defparam point-sym Point-Sym 'circle)
 (defparam point-color Plot-Color 0)
+(defparam point-x-jitter Real 0)
+(defparam point-y-jitter Real 0)
+(defparam point-z-jitter Real 0)
 (defparam2 point-size Real Nonnegative-Real 6 (nonnegative-rational 'point-size))
 (defparam2 point-line-width Real Nonnegative-Real 1 (nonnegative-rational 'point-line-width))
 (defparam2 point-alpha Real Nonnegative-Real 1 (unit-ivl 'point-alpha))
diff --git a/plot-lib/plot/private/plot2d/point.rkt b/plot-lib/plot/private/plot2d/point.rkt
index 582561d2..865e2c7a 100644
--- a/plot-lib/plot/private/plot2d/point.rkt
+++ b/plot-lib/plot/private/plot2d/point.rkt
@@ -39,6 +39,8 @@
           #:sym Point-Sym
           #:color Plot-Color
           #:fill-color (U Plot-Color 'auto)
+          #:x-jitter Nonnegative-Real
+          #:y-jitter Nonnegative-Real
           #:size Nonnegative-Real
           #:line-width Nonnegative-Real
           #:alpha Nonnegative-Real
@@ -50,6 +52,8 @@
                 #:sym [sym (point-sym)]
                 #:color [color (point-color)]
                 #:fill-color [fill-color 'auto]
+                #:x-jitter [x-jitter (point-x-jitter)]
+                #:y-jitter [y-jitter (point-y-jitter)]
                 #:size [size (point-size)]
                 #:line-width [line-width (point-line-width)]
                 #:alpha [alpha (point-alpha)]
@@ -67,16 +71,19 @@
             [vs  (filter vrational? vs)])
        (cond
          [(empty? vs)  (renderer2d #f #f #f #f)]
-         [else  (match-define (list (vector #{xs : (Listof Real)} #{ys : (Listof Real)}) ...) vs)
-                (let ([x-min  (if x-min x-min (apply min* xs))]
-                      [x-max  (if x-max x-max (apply max* xs))]
-                      [y-min  (if y-min y-min (apply min* ys))]
-                      [y-max  (if y-max y-max (apply max* ys))]
-                      [fill-color  (if (eq? fill-color 'auto) (->pen-color color) fill-color)])
-                  (renderer2d
-                   (vector (ivl x-min x-max) (ivl y-min y-max)) #f default-ticks-fun
-                   (points-render-fun vs sym color fill-color
-                                      size line-width alpha label)))]))]))
+         [else
+          (unless (= 0 x-jitter y-jitter)
+            (points-apply-jitters vs (vector x-jitter y-jitter) #:ivls (vector (ivl x-min x-max) (ivl y-min y-max))))
+          (match-define (list (vector #{xs : (Listof Real)} #{ys : (Listof Real)}) ...) vs)
+          (let ([x-min  (if x-min x-min (apply min* xs))]
+                [x-max  (if x-max x-max (apply max* xs))]
+                [y-min  (if y-min y-min (apply min* ys))]
+                [y-max  (if y-max y-max (apply max* ys))]
+                [fill-color  (if (eq? fill-color 'auto) (->pen-color color) fill-color)])
+            (renderer2d
+             (vector (ivl x-min x-max) (ivl y-min y-max)) #f default-ticks-fun
+             (points-render-fun vs sym color fill-color
+                                size line-width alpha label)))]))]))
 
 ;; ===================================================================================================
 ;; Vector fields
diff --git a/plot-lib/plot/private/plot3d/point.rkt b/plot-lib/plot/private/plot3d/point.rkt
index 893af09f..8436127e 100644
--- a/plot-lib/plot/private/plot3d/point.rkt
+++ b/plot-lib/plot/private/plot3d/point.rkt
@@ -39,6 +39,9 @@
           #:sym Point-Sym
           #:color Plot-Color
           #:fill-color (U Plot-Color 'auto)
+          #:x-jitter Nonnegative-Real
+          #:y-jitter Nonnegative-Real
+          #:z-jitter Nonnegative-Real
           #:size Nonnegative-Real
           #:line-width Nonnegative-Real
           #:alpha Nonnegative-Real
@@ -51,6 +54,9 @@
                   #:sym [sym (point-sym)]
                   #:color [color (point-color)]
                   #:fill-color [fill-color 'auto]
+                  #:x-jitter [x-jitter (point-x-jitter)]
+                  #:y-jitter [y-jitter (point-y-jitter)]
+                  #:z-jitter [z-jitter (point-z-jitter)]
                   #:size [size (point-size)]
                   #:line-width [line-width (point-line-width)]
                   #:alpha [alpha (point-alpha)]
@@ -70,6 +76,11 @@
             [vs  (filter vrational? vs)])
        (cond [(empty? vs)  (renderer3d #f #f #f #f)]
              [else
+              (unless (= 0 x-jitter y-jitter z-jitter)
+                (points-apply-jitters vs (vector x-jitter y-jitter z-jitter)
+                                      #:ivls (vector (ivl x-min x-max)
+                                                     (ivl y-min y-max)
+                                                     (ivl z-min z-max))))
               (match-define (list (vector #{xs : (Listof Real)}
                                           #{ys : (Listof Real)}
                                           #{zs : (Listof Real)})
diff --git a/plot-lib/plot/private/utils-and-no-gui.rkt b/plot-lib/plot/private/utils-and-no-gui.rkt
index 471a805c..3c5ef2a3 100644
--- a/plot-lib/plot/private/utils-and-no-gui.rkt
+++ b/plot-lib/plot/private/utils-and-no-gui.rkt
@@ -126,6 +126,9 @@
  point-sym
  point-color
  point-size
+ point-x-jitter
+ point-y-jitter
+ point-z-jitter
  point-line-width
  point-alpha
  vector-field-samples
diff --git a/plot-lib/plot/utils.rkt b/plot-lib/plot/utils.rkt
index 4fc85bd0..7b950233 100644
--- a/plot-lib/plot/utils.rkt
+++ b/plot-lib/plot/utils.rkt
@@ -80,6 +80,7 @@
  ivl-translate
  bounds->intervals
  clamp-real
+ points-apply-jitters
  ;; Rectangles
  Rect
  rect-meet