diff --git a/lib/dynamic_image/helper.rb b/lib/dynamic_image/helper.rb
index 426d951..2479b83 100644
--- a/lib/dynamic_image/helper.rb
+++ b/lib/dynamic_image/helper.rb
@@ -54,9 +54,11 @@ def dynamic_image_path(record_or_array, options = {})
     #   # => <img alt="Avatar" src="..." width="100" height="62" />
     def dynamic_image_tag(record_or_array, options = {})
       record = extract_dynamic_image_record(record_or_array)
+      requested = options[:size]
       size = fit_size!(record_or_array, options)
       url_options = options.extract!(*allowed_dynamic_image_url_options)
-      html_options = { size:, alt: record.alt_text }.merge(options)
+      html_options = { size: display_size(size, requested), alt: record.alt_text }
+                     .merge(options)
 
       image_tag(dynamic_image_path_with_size(record_or_array,
                                              size,
@@ -78,8 +80,8 @@ def dynamic_image_tag(record_or_array, options = {})
     #   an array is negotiated against the image by {DynamicImage::FormatNegotiator}. Defaults to
     #   {DynamicImage.default_formats}, or {DynamicImage.mailer_formats} in a mailer view.
     # @return [String]
-    # @raise [DynamicImage::Errors::InvalidSizeOptions] if <tt>crop: true</tt> is given without both dimensions, or
-    #   if the size works out to less than a pixel
+    # @raise [DynamicImage::Errors::InvalidSizeOptions] if the size is zero on both axes, or if <tt>crop: true</tt>
+    #   is given without both dimensions or leaves less than a pixel to render
     #
     # Any options supported by +polymorphic_url+ are also accepted.
     #
@@ -218,7 +220,16 @@ def fit_size!(record_or_array, options)
     def image_sizing(record, size_opts, uncropped)
       ImageSizing
         .new(record, uncropped:)
-        .fit(size_opts[:size], size_opts).floor.to_s
+        .fit_renderable(size_opts[:size], size_opts).floor.to_s
+    end
+
+    # Ensure either dimension is at least 1px
+    def display_size(size, requested)
+      return size unless requested
+
+      Vector2d.parse(size)
+              .fit(Vector2d.parse(requested), upscale: false)
+              .floor.max(1).to_s
     end
   end
 end
diff --git a/lib/dynamic_image/helper/pictures.rb b/lib/dynamic_image/helper/pictures.rb
index 22da663..994046b 100644
--- a/lib/dynamic_image/helper/pictures.rb
+++ b/lib/dynamic_image/helper/pictures.rb
@@ -45,6 +45,8 @@ def dynamic_picture(record_or_array, options = {})
       # @option options [Integer] :fallback_width The width to ask for the <tt>img</tt>, overriding
       #   {DynamicImage.picture_fallback_width}
       # @return [String] the picture element
+      # @raise [DynamicImage::Errors::InvalidSizeOptions] if the image has less than a pixel to render at the
+      #   requested ratio
       #
       # @example
       #   dynamic_picture_tag(image, sizes: "50vw", alt: "A kitten")
diff --git a/lib/dynamic_image/image_sizing.rb b/lib/dynamic_image/image_sizing.rb
index bcc676b..5040482 100644
--- a/lib/dynamic_image/image_sizing.rb
+++ b/lib/dynamic_image/image_sizing.rb
@@ -114,30 +114,59 @@ def fit(fit_size, options = {})
       fit_size
     end
 
+    # Fits the size like {#fit}, but returns the smallest size the image can be rendered at rather than raising when
+    # the result lands under a pixel.
+    #
+    # @param fit_size [Vector2d, String] the size to fit within, as taken by {#fit}
+    # @param options [Hash] as taken by {#fit}
+    # @return [Vector2d] the resulting size
+    # @raise [DynamicImage::Errors::InvalidSizeOptions] if the size is zero on both axes, or if <tt>crop: true</tt>
+    #   is given and the crop is less than a pixel
+    #
+    # @example
+    #   image = Image.find(params[:id]) # 2000x1 image
+    #   sizing = DynamicImage::ImageSizing.new(image)
+    #
+    #   sizing.fit_renderable("1200x") # => Vector2d(2000.0, 1.0)
+    def fit_renderable(fit_size, options = {})
+      require_nonzero!(parse_vector(fit_size))
+      return fit(fit_size, options) if options[:crop] || renderable?(fit_size, options)
+
+      size.cover(1).round
+    end
+
+    # Returns true if the image can be rendered at +fit_size+, false if {#fit} rejects it.
+    #
+    # @param fit_size [Vector2d, String] the size to fit within, as taken by {#fit}
+    # @param options [Hash] as taken by {#fit}
+    # @return [Boolean]
+    #
+    # @example
+    #   image = Image.find(params[:id]) # 320x200 image
+    #   sizing = DynamicImage::ImageSizing.new(image)
+    #
+    #   sizing.renderable?(Vector2d(100, 0)) # => true
+    #   sizing.renderable?(Vector2d(1, 0))   # => false
+    def renderable?(fit_size, options = {})
+      vector = parse_vector(fit_size)
+      return false if options[:crop] && !(vector.x.positive? && vector.y.positive?)
+      return false if vector.x.zero? && vector.y.zero?
+
+      pixels?(snap(scale(vector, options)))
+    end
+
     private
 
     def crop_gravity
-      if uncropped? && !record.crop_gravity?
-        size / 2
-      else
-        record.crop_gravity
-      end
+      uncropped? && !record.crop_gravity? ? size / 2 : record.crop_gravity
     end
 
     def crop_start
-      if uncropped?
-        Vector2d.new(0, 0)
-      else
-        record.crop_start
-      end
+      uncropped? ? Vector2d.new(0, 0) : record.crop_start
     end
 
     def size
-      if uncropped?
-        record.real_size
-      else
-        record.size
-      end
+      uncropped? ? record.real_size : record.size
     end
 
     # Clamps the rectangle defined by +start+ and +size+ to fit inside 0, 0 and +max_size+. It is assumed that +size+
@@ -182,12 +211,16 @@ def require_nonzero!(vector)
     # Rejects sizes that don't round to at least one pixel in each dimension, since there is no image to render at
     # that point.
     def require_pixels!(vector)
-      return if vector.x >= 1 && vector.y >= 1
+      return if pixels?(vector)
 
       raise DynamicImage::Errors::InvalidSizeOptions,
             "#{vector} has a dimension smaller than one pixel"
     end
 
+    def pixels?(vector)
+      vector.x >= 1 && vector.y >= 1
+    end
+
     def shift_vector(vect)
       Vector2d.new(
         vect.x.negative? ? vect.x.abs : 0,
diff --git a/lib/dynamic_image/picture.rb b/lib/dynamic_image/picture.rb
index d97f510..c1809cb 100644
--- a/lib/dynamic_image/picture.rb
+++ b/lib/dynamic_image/picture.rb
@@ -28,7 +28,7 @@ class Picture
     # @!attribute [r] breakpoints
     #   @return [DynamicImage::Breakpoints] the candidate widths
     # @!attribute [r] fallback_width
-    #   @return [Integer] the width asked for the fallback image
+    #   @return [Integer] the width configured for the fallback image
     attr_reader :template, :record_or_array, :ratio, :sizes, :breakpoints, :fallback_width, :url_options
 
     # @param template [ActionView::Base] the view context, for routing
@@ -77,9 +77,13 @@ def available_width
 
     # The candidate widths, smallest first.
     #
+    # Widths the image can't be rendered at are left out. One that can't be rendered at any of them gets a single
+    # candidate at its available width.
+    #
     # @return [Array<Integer>]
     def widths
-      @widths ||= breakpoints.widths(available_width)
+      @widths ||= breakpoints.widths(available_width).select { renderable?(it) }.presence ||
+                  [available_width].select { renderable?(it) }
     end
 
     # Every candidate, as the URL and the size it is actually rendered at.
@@ -128,9 +132,12 @@ def fallback_format
 
     # The size asked for the fallback image, as a <tt>"{width}x{height}"</tt> string.
     #
+    # This is {#fallback_width}, unless the image can't be rendered that wide, in which case the widest candidate
+    # it can be rendered at stands in.
+    #
     # @return [String]
     def fallback_size
-      @fallback_size ||= size_for(fallback_width)
+      @fallback_size ||= size_for(renderable?(fallback_width) ? fallback_width : (widths.last || fallback_width))
     end
 
     # The size the fallback image is actually rendered at. Smaller than {#fallback_size} when the image is.
@@ -171,6 +178,10 @@ def breakpoints_from(options)
       DynamicImage::Breakpoints.new(options[:breakpoints], step: options[:step])
     end
 
+    def renderable?(width)
+      sizing.renderable?(size_for(width), crop: crop?)
+    end
+
     def record
       record_or_array.last
     end
diff --git a/spec/dynamic_image/helper/pictures_spec.rb b/spec/dynamic_image/helper/pictures_spec.rb
index 9e2141c..b5cd670 100644
--- a/spec/dynamic_image/helper/pictures_spec.rb
+++ b/spec/dynamic_image/helper/pictures_spec.rb
@@ -89,6 +89,15 @@ def fixture(name, content_type)
       end
     end
 
+    context "with an extremely wide image" do
+      # 1000x2, less than a pixel tall at any of the breakpoints
+      let(:image) { Image.create(file: fixture("wide.png", "image/png")) }
+
+      it "renders the widths it can, rather than raising" do
+        expect(markup).to include('width="1000" height="2"')
+      end
+    end
+
     context "with an animated image" do
       let(:image) { Image.create(file: fixture("animated.gif", "image/gif")) }
       let(:options) { {} }
diff --git a/spec/dynamic_image/helper_spec.rb b/spec/dynamic_image/helper_spec.rb
index 192412d..0b4d1a9 100644
--- a/spec/dynamic_image/helper_spec.rb
+++ b/spec/dynamic_image/helper_spec.rb
@@ -43,6 +43,28 @@ def generate_digest(str)
       end
     end
 
+    context "with an image too wide to render that small" do
+      # 1000x2
+      let(:image) do
+        Image.create(
+          file: Rack::Test::UploadedFile.new(
+            File.open(File.expand_path("../support/fixtures/wide.png",
+                                       __dir__)),
+            "image/png"
+          )
+        )
+      end
+      let(:options) { { size: "400x" } }
+
+      it "renders the smallest size that holds the whole frame" do
+        expect(tag).to include("/500x1/")
+      end
+
+      it "lays it out at the size asked for" do
+        expect(tag).to include('width="400" height="1"')
+      end
+    end
+
     context "with HTML options" do
       let(:options) { { size: "100x100", alt: "Foobar", class: "foo" } }
       let(:digest) { generate_digest("show-#{image.id}-100x62") }
diff --git a/spec/dynamic_image/image_sizing_spec.rb b/spec/dynamic_image/image_sizing_spec.rb
index 11d37f6..a526d5b 100644
--- a/spec/dynamic_image/image_sizing_spec.rb
+++ b/spec/dynamic_image/image_sizing_spec.rb
@@ -314,4 +314,74 @@ def v(width, height)
       it { is_expected.to eq(v(520, 500)) }
     end
   end
+
+  describe "#fit_renderable" do
+    subject(:renderable) { sizing.fit_renderable(v(100, 100)) }
+
+    it { is_expected.to eq(v(100, 62.5)) }
+
+    context "when the result is less than a pixel tall" do
+      subject(:renderable) { sizing.fit_renderable(v(1, 1)) }
+
+      it { is_expected.to eq(v(2, 1)) }
+    end
+
+    context "with an extremely wide image" do
+      subject(:renderable) { sizing.fit_renderable("400x") }
+
+      let(:real_size) { v(1000, 2) }
+
+      it { is_expected.to eq(v(500, 1)) }
+    end
+
+    context "with an extremely tall image" do
+      subject(:renderable) { sizing.fit_renderable("x400") }
+
+      let(:real_size) { v(2, 1000) }
+
+      it { is_expected.to eq(v(1, 500)) }
+    end
+
+    context "with a crop that leaves less than a pixel" do
+      let(:real_size) { v(1000, 2) }
+
+      it "raises an error" do
+        expect { sizing.fit_renderable(v(1, 3), crop: true) }.to(
+          raise_error(DynamicImage::Errors::InvalidSizeOptions)
+        )
+      end
+    end
+
+    context "with an empty size" do
+      it "raises an error" do
+        expect { sizing.fit_renderable("x") }.to(
+          raise_error(DynamicImage::Errors::InvalidSizeOptions)
+        )
+      end
+    end
+  end
+
+  describe "#renderable?" do
+    subject(:renderable) { sizing.renderable?(v(100, 0)) }
+
+    it { is_expected.to be(true) }
+
+    context "when the result is less than a pixel tall" do
+      subject(:renderable) { sizing.renderable?(v(1, 0)) }
+
+      it { is_expected.to be(false) }
+    end
+
+    context "with an extremely wide image" do
+      let(:real_size) { v(1000, 2) }
+
+      it { is_expected.to be(false) }
+    end
+
+    context "when the options rule the size out" do
+      subject(:renderable) { sizing.renderable?(v(100, 0), crop: true) }
+
+      it { is_expected.to be(false) }
+    end
+  end
 end
diff --git a/spec/dynamic_image/images_controller_spec.rb b/spec/dynamic_image/images_controller_spec.rb
index 6ad29c8..dd3cb30 100644
--- a/spec/dynamic_image/images_controller_spec.rb
+++ b/spec/dynamic_image/images_controller_spec.rb
@@ -146,6 +146,28 @@ def get_original(image, format)
       end
     end
 
+    context "with a size only a pixel tall" do
+      # 1000x2, which is what a candidate width of 510 comes to
+      let(:image) do
+        Image.create(
+          file: Rack::Test::UploadedFile.new(
+            File.open(File.expand_path("../support/fixtures/wide.png",
+                                       __dir__)),
+            "image/png"
+          )
+        )
+      end
+
+      before do
+        get :show,
+            params: digested(:show, id: image.id, size: "510x1", format: :png)
+      end
+
+      it "renders it" do
+        expect(metadata.dimensions).to eq(Vector2d.new(510, 1))
+      end
+    end
+
     context "when format is GIF" do
       before do
         get :show,
diff --git a/spec/dynamic_image/picture_spec.rb b/spec/dynamic_image/picture_spec.rb
index a406391..1ad1f5b 100644
--- a/spec/dynamic_image/picture_spec.rb
+++ b/spec/dynamic_image/picture_spec.rb
@@ -56,6 +56,26 @@ def fixture(name, content_type)
         expect(picture.widths).to eq([110, 160, 220, 320])
       end
     end
+
+    context "with an extremely wide image" do
+      # 1000x2
+      let(:image) { Image.create(file: fixture("wide.png", "image/png")) }
+      let(:options) { { breakpoints: 100..1000, step: 1.4 } }
+
+      it "leaves out the widths it would be less than a pixel tall at" do
+        expect(picture.widths).to eq([510, 710, 1000])
+      end
+    end
+
+    context "with an image too wide for any of the breakpoints" do
+      # 1000x2
+      let(:image) { Image.create(file: fixture("wide.png", "image/png")) }
+      let(:options) { { breakpoints: 100..320, step: 1.4 } }
+
+      it "offers a single candidate at its own width" do
+        expect(picture.widths).to eq([1000])
+      end
+    end
   end
 
   describe "#variants" do
@@ -78,6 +98,16 @@ def fixture(name, content_type)
         expect(picture.variants.last).to include(width: 200, height: 200)
       end
     end
+
+    context "with an extremely wide image" do
+      # 1000x2
+      let(:image) { Image.create(file: fixture("wide.png", "image/png")) }
+      let(:options) { { breakpoints: 100..1000, step: 1.4 } }
+
+      it "advertises a whole pixel of height" do
+        expect(picture.variants.pluck(:height)).to eq([1, 1, 2])
+      end
+    end
   end
 
   describe "#srcset" do
@@ -203,6 +233,20 @@ def fixture(name, content_type)
 
       it { expect(picture.width).to eq(100) }
     end
+
+    context "when the image is too wide to render at the width asked for" do
+      # 1000x2
+      let(:image) { Image.create(file: fixture("wide.png", "image/png")) }
+      let(:options) { { breakpoints: 100..1000, step: 1.4, fallback_width: 100 } }
+
+      it "asks for the widest candidate it can render instead" do
+        expect(picture.fallback_size).to eq("1000x")
+      end
+
+      it "reserves a box at least a pixel tall" do
+        expect([picture.width, picture.height]).to eq([1000, 2])
+      end
+    end
   end
 
   describe "url options" do
diff --git a/spec/support/fixtures/wide.png b/spec/support/fixtures/wide.png
new file mode 100644
index 0000000..239bb51
Binary files /dev/null and b/spec/support/fixtures/wide.png differ